ABSTRACT. To better apprehend the improved mechanical properties of highly structured multi-nanolayer films obtained by co-extrusion, as well as identifying the key parameters governing their structure-morphology, the present study focuses on model films made of low-density polyethylene (LDPE) and polystyrene (PS). Despite being two immiscible polymers with highly-mismatched rheological behavior (and without the need of compatibilizers), coextrusion by forced-layer-assembly allows to prepare well-controlled multilayer films with different level of confinement through the fine tuning of their number of layers. More specifically, the layer confinement of a semi-crystalline polymer, here LDPE, by a glassy amorphous polymer, here PS, was investigated. In comparison to each of the two base materials, the obtained multilayer architecture brings out the best of the two worlds by combining the ductility of LDPE with the high strength of PS, greatly outperforming the corresponding 50/50 randomly structured blend. Interestingly, we have demonstrated that increasing the number of layers of PS/LDPE system (while remaining in the processing window of stable continuous layers), thus increasing the level of layer confinement, allows to stabilize the brittle damage mechanisms (i.e. crazes) of PS, enabling to reach large strains without macroscopic failure. In parallel to the multi-layer morphology characterization by SEM and TEM, the orientation and crystalline structure of the coextruded films were also characterized by WAXS and DSC. The geometrical confinement of LDPE nanolayer did not affect the thermal properties of LDPE crystalline phase, but it did affect its crystalline morphology, evolving from an isotropic-spherulitic shape to a more lamellae-oriented form.

ABSTRACT. ISO 23228:2011[1] proposed a testing method in which the plastic material, experimental resins or compounds for pipes and fittings, can be exposed to stress conditions that mimic internally pressurized end-capped pipes. The stress conditions are mimicked by the use of a plaque specimen having a grooved reduced section called plane strain grooved tensile (PSGT) specimens producing a bi-axial state of stress under uni-axial loading.

In this study, PSGT specimens were cut-out from HDPE pipes. Two shape ratios, ratio between the width and the groove thickness, equal to 20 and 25, were used. Both the axial and transverse displacements and strain fields were followed by a Digital Image Correlation (DIC) camera during tensile and creep loading, both at room and high temperature.

The increasing effect of the temperature in both the axial and transverse displacement and strain was noticed; conversely, no significant effect of the width was highlighted. The results have evidenced that, as the plane-strain condition in the width is assured during the tests, PSGT specimens can be used to mimic internally pressurized pipes under monotonic increasing or constant-in-time loading at both room and high temperature, but it must be better to use specimens with a higher shape ratio, i.e. higher width[2]. The results, which will be discussed during the presentation, contribute to the 9th Sustainable Development Goal: Industry, Innovation and Infrastructure, by promoting a sustainable industrialization and fostering innovation.

REFERENCES [1] ISO/TC 138, Thermoplastics pipes for the conveyance of fluids – Determination of the stress-rupture resistance of moulding materials using plain strain grooved tensile (PSGT) specimens, 23228:2011(E), 2011. [2] C. Ovalle, M. Broudin, L. Laiarinandrasana, Plane–strain condition in plane–strain grooved tensile (PSGT) specimens during traction and creep loading at room and high temperature, Strain 2023, e12467.

ABSTRACT. Packaging steels are coated with the polymer PET for preserving content quality, preventing corrosion, and enabling printability on the surface. The industrial lamination process must handle large volumes at high speeds, imposing a critical challenge. At elevated production speeds, air bubbles are entrapped between the polymer coating and the steel substrate, significantly impacting the final product's quality. The physics governing this air entrapment process are poorly understood, and establishing the relationship with overall process parameters is crucial.

In this presentation, we will address the air entrapment problem using a two-scale finite element modeling strategy, complemented by experiments. The coarse-scale model is developed to establish the connection between processing parameters (line speed, roll pressure, temperature, etc.) and the actual loading conditions in the lamination nip where the polymer film bonds. The fine-scale model delves into the roughness asperities of the steel sheet, explicitly studying the plastic flow of the film at high temperatures and strain rates into the roughness valleys.

The Eindhoven Glassy Polymer (EGP) is employed to model the behavior of PET under extreme rate/temperature conditions, where thermo-mechanical parameters are taken from literature or calibrated through experiments. The results from the two-scale finite element model reveal that air bubble formation is highest when the temperature of the substrate steel is low or the lamination speed is high. The model allows us to establish a quantitative link between macro-scale process parameters and incomplete filling or bonding of PET at the micro-scale. This paves the way for controlling the air entrapment, thereby enhancing the quality of the coated steels.

ABSTRACT. Polymeric foams are widely used in different industries such as automotive, aviation and military due to their wide density range, high specific strength, strong ability to absorb impact loads, and good thermal insulation properties. In this study, taking advantage of 3D imaging technology based on X-ray computed tomography (CT), in-situ compression tests were carried out to explore the global and local deformation behaviour of open cell polyurethane foams. Different strain levels were recorded, and relevant images were reconstructed from x-ray CT during the in-situ tests. To better understand the deformation behaviour of the interior structure of foams under uniaxial loading, the CT image-based finite element method is widely used which provides a non-destructive and non-invasive way to obtain the real internal structure of the foam for different loading stage. An advanced image-based finite element analysis method was proposed in this study. The finite element models of foam microstructures were generated from images obtained by X-ray CT by applying level set method (LSM) and Delaunay triangulation (DT). Moreover, to improve the mesh quality of the FE models and calculation accuracy, Taubin smoothing was utilized. Then, numerical simulations on the smoothed mesh were implemented to compare with the experimental tests and understand deformation process during compression. Good agreement was observed between the deformations obtained by simulations and in-situ compression experiments at different strain levels. Morphological features of deformed models at different strain level were identified. Three main features were analysed, namely: strut length, strut thickness and strut orientation. The comparison of these features for different deformation stages was carried out. The results suggest that, under uniaxial stress, the open-cell foam deforms by struts bending followed, at sufficiently large loads, by nonlinear deformation within the struts. The deformation behaviour of the interior structure strongly depends on the initial orientation and thickness of struts.

ABSTRACT. Filled elastomer networks are reported to dissipate energy when subjected to cyclic tension or compression tests. Mullins effect is considered the main contributor to this dissipation during the first loading-unloading cycle. At the same time, other mechanisms, such as damage, viscosity, and strain-induced crystallisation, contribute to the long-term energy dissipation. A recent study attributed the Mullins effect to the covalent bond scission in filled silica polydimethylsiloxane (PDMS) using mechanoluminescent cross-linkers during cyclic uniaxial tests. In contrast, little work has been reported on the cyclic response at the micrometre scale, particularly in silica-filled PDMS. In this presentation, we use cyclic nanoindentation tests to study the mechanical behaviour of room-temperature vulcanised (RTV) PDMS at a small scale. Its mechanical behaviour under cyclic uniaxial tensile tests is also investigated. The considered RTV PDMS is filled with SiO2 (50phr) and CaCO3 (10phr). Moreover, the samples are thermally aged between 30°C and 70°C from 10 to 300 days. The dissipative work is quantified as the hysteresis between loading and unloading cycles. Additional stress relaxation tensile tests have been performed to discriminate viscoelastic relaxation and Mullins behaviours during unloading phases, as they are likely to simultaneously contribute to this energy dissipation. The results of tensile tests show negligible viscoelastic relaxation while the Mullins effect is dominant. The above result is used to analyse the local mechanical behaviour of the virgin material surface. Numerous indentation tests are carried out to study the hysteresis area. Hysteretic dissipation is compared at both scales. Thermal ageing influences the evolution of the hysteresis area characterised in both tests.

ABSTRACT. Energy absorption structures in both motorsport and aerospace applications are nowadays manufactured using carbon fibre reinforced polymer (CFRP) materials. Several new composite materials have been recently introduced to the market, including thin-ply CFRPs and more environmentally sustainable alternatives, such as thermoplastics and natural fibre composites (NFCs). There is a noticeable knowledge gap about the energy absorption capabilities of these novel materials, limiting their potential introduction to the design of such structures. While it is known that NFC materials such as flax fibre thermosets possess significantly lower mechanical properties (e.g. compressive strength) compared to high-grade CFRPs, energy absorption is not a simple reflection of these base properties, and thus such materials should not be disregarded at first glance. Furthermore, through laminate hybridisation, there is a realistic potential of matching the energy absorption offered by classical CFRPs while incurring a minimal weight penalty and simultaneously improving the sustainability of the structure. The present work aims to study the crashworthiness performance of hybrid composite laminates manufactured from thermoset NFCs and CFRPs. A quasi-static experimental study was performed on both monolithic and hybrid laminate tubular coupons of various curvatures. These were crushed in a stable progressive manner, enabling the determination of a steady-state crush stress and a corresponding specific energy absorption. Significant improvements were noted in the energy absorption levels of both monolithic flax and hybrid laminate coupons, in comparison to those presented in literature. Furthermore, a hybrid laminate Formula 1 Side Impact Structure (SIS) was manufactured and tested in collaboration with McLaren Racing, as a first demonstration of the potential use of NFCs in similar crashworthiness applications.

ABSTRACT. A pin-ended buckling test inspired by Wisnom's [1] has been developed to evaluate the effect of the strain gradient on the compressive failure strain for composite laminates. Tests were carried out on UD carbon/epoxy AS4/8552 composite on open hole and plain specimens. Strains were measured using digital image correlation. Besides, an infrared camera was used to follow visible material damages and kink-band propagation. Different cross ply stacking sequences [(0/90)4]S, [02/(90/0)3]S, [04/(90/0)2]S and [(0/90)8]S, [(0/90)4]S, [(0/90)2]S were tested to investigate both the effect of the thickness of the outer 0° ply and of the thickness specimen on the compressive failure strain. Initial results on plain specimens show a non-linear behaviour in the increase of the compressive strain failure as a function of the strain gradient for the material studied, which does not accord with Wisnom’s results which showed a linear trend. Secondly, most of the plain specimen failed in the tension side, due to the high compressive strenght helped by the strain gradient, and at the same time the tension failure strain remains unaffected by the strain gradient. Open hole specimens add the presence of an in-plane strain gradient due the stress concentration at the hole edge. The results of the open hole specimens show that the presence of the hole helps compressive failure, since all the specimens failed in compressive side whereas the same plain specimens failed in tension. Despite the second plane gradient, the open holes specimens seem to have less of a gradient effect than the plain ones. [1] Wisnom, M. R., J. W. Atkinson, et M. I. Jones. 1997. « Reduction in Compressive Strain to Failure with Increasing Specimen Size in Pin-Ended Buckling Tests ». Composites Science and Technology 57(9 10):1303 8. doi: 10.1016/S0266-3538(97)00057-2

ABSTRACT. Mechanical fasteners are still a fast and effective way of joining composite components and subcomponents. The mechanical properties and associated failure modes for such joints can be characterised following the ASTM D5961 standard. More recently some mechanical joint designs have included an additional design case catering for controlled energy absorption, such as the tension-absorbers deployed in aeronautical applications. These joints offer a sustained level of energy absorption through an extended bearing failure mode, leading to controlled crushing, while avoiding the undesired fastener pull-out through the composite thickness. To date these fastened joints have been designed using more conventional thermoset resin carbon-fibre composites. A number of new material systems have recently been introduced in the transportation sector, including thin-ply CFRPs, as well as more environmentally sustainable alternatives, such as thermoplastics and natural fibre composites (NFCs). This work aims to study the energy absorption performance of an advanced thermoplastic system employed in fastened joints. A quasi-static experimental study was conducted, including bearing and extended bearing tests. This study also investigates the influence of the tightened fastener, through independent coupon testing of both pinned and fastened joints. A stable crushing stress corresponding to approximately 50% of the peak bearing stress for pinned joints is observed, in line with the observed results in the literature for thermoset matrix composites. The employment of a bolted joint leads to an increase in peak and crushing bearing stresses of approximately 100% with respect to the pinned joint, caused by the confinement of the crash front and suppression of delamination. In addition, different specimen geometries were studied, focusing on the variation of the overall w/D (width/hole diameter) ratio, showing its effect on the failure mode transition from the desired bearing to net tension failure by split cracking, net-section delamination, and fibre tensile failure.

ABSTRACT. Thin-ply composites (t_ply=20-80 g/m^2) are gaining popularity due to their minimal manufacturing defects and uniform mechanical properties. However, they suffer from increased brittleness and notchsensitivity due to reduced strain redistribution capabilities [1]. Hybridisation using Low Elongation (LE) and High Elongation (HE) layers, specifically the [HE/LE/HE] sub-laminate design, introduces pseudo-ductility by inducing fragmentation in the LE layer, leading to a metal-like behaviour. However, the relationship between ply thickness, translaminar toughness, and notch sensitivity complicates ascertaining the improvements solely attributable to pseudo-ductility [2, 3]. Studies by Czél and Tavares highlight a reduction in notch sensitivity in hybrid laminates but with varying results depending on specimen size and design [4, 5]. This study develops pseudo-ductile hybrid laminates without significantly increasing sub-laminate thickness, ensuring comparable unnotched tensile strength to the LE counterpart of the same laminate stacking sequence. We characterised the unnotched and notched strengths of both laminates, employing Digital Image Correlation (DIC) to analyse damage mechanisms. Then, we identified and analysed strain non-linearities using the DIC images to differentiate the damage mechanisms in both laminate types. Further, we also employed DIC to examine full-field pseudo-ductile strains and damage incrementally. Our findings provide a clear pathway to delineate and compare damage mechanisms between reference and hybrid materials, showcasing the effectiveness of our proposed methodology.

References [1] Amacher, R., Cugnoni, J., Botsis, J., Sorensen, L., Smith, W., & Dransfeld, C. (2014). Thin ply composites: Experimental characterization and modeling of size-effects. Composites Science and Technology, 101, 121-132. [2] Furtado, C., Arteiro, A., Linde, P., Wardle, B. L., & Camanho, P. P. (2020). Is there a ply thickness effect on the mode I intralaminar fracture toughness of composite laminates?. Theoretical and Applied Fracture Mechanics, 107, 102473. [3] Subramani, A., Maimí, P., Guerrero, J. M., & Costa, J. (2023). Nominal strength of notched seudo-ductile specimens. Theoretical and Applied Fracture Mechanics, 128, 104120. [4] Czél, G., Jalalvand, M., Fotouhi, M., Longana, M. L., Nixon-Pearson, O. J., & Wisnom, M. R. (2018). Pseudo-ductility and reduced notch sensitivity in multi-directional all-carbon/epoxy thin-ply hybrid composites. Composites Part A: Applied Science and Manufacturing, 104, 151-164. [5] Tavares, R. P. (2020). Mechanics of deformation and failure of fibre hybrid composites (Doctoral dissertation, Universidade do Porto (Portugal))

ABSTRACT. The use of LH2 as a possible alternative for a sustainable propellant in the aeronautic industry represents a major step for developing a zero-emissions aircraft. This fuel must be stored and handled at cryogenic temperatures. Therefore, composite structures under cryogenic temperatures has become a interesting scientific and industrial topic in recent years. The influence of cryogenic temperatures on material performance has to be investigated including different loading scenarios such as impact events.

On this work, authors have characterized Carbon Fiber Reinforced Polymer (CFRP) laminates under quasistatic and dynamic conditions for ambient and cryogenic temperatures (-150ºC). Characterisation campaign is focused on the transversal and off-axis behaviour of CFRP laminate under compressive loadings. For dynamic conditions, a Split-Hopkinson Pressure Bar (SHPB) has to be used in order to reach strain rate up to 500 1/s. Moreover, drop weight tower test has been performed for ambient and cryogenic temperatures (-150ºC) at quasi-isotropic laminates. Finally, after an ultrasonic inspection, compression after impact test has been carried out to evaluate the residual performance of the impacted laminated. The analysis of the complete testing campaign deepen the understanding of the performance of the matrix and matrix-fibres interaction under these extreme conditions.

ABSTRACT. The post-impact strength of CFRP composite materials stands as a crucial design parameter for aeronautical structures, dictating their damage tolerance. In low velocity impact tests, the laminate demonstrates a partial return of energy to the indenter above a certain threshold, exhibiting elastic recovery. The remaining energy undergoes absorption and dissipation within the laminate, manifesting as damage (both interlaminar and intralaminar), plastic deformation of the polymer matrix, and breakage of carbon fibers. Despite its significance, quantifying the contribution of individual damage mechanisms to the overall energy absorption process remains a challenge due to experimental complexities. Herein, we introduce a novel experimental approach leveraging local induction heating to isolate the influence of fiber breakage during the damage process. This methodology mimics the extent and location of damage incurred in standard low-velocity impacts while preserving fiber integrity. Our study compares the residual strength and stiffness of AS4/PEEK laminates subjected to impacts across a range of energies (20-70J) with those damaged by electromagnetic currents, ensuring equivalent damage extensions. The findings underscore the profound impact of carbon fiber breakage on laminate stiffness, while strength remains largely unaffected. This reaffirms delamination as the primary contributor to strength loss in post-impact compression scenarios.

ABSTRACT. Martensite damage in Dual-Phase steel has been analyzed extensively, but the exact deformation mechanisms that trigger or prevent damage initiation remain mostly unexplored. Whereas generally assumed to be hard and brittle, ‘1D’ nano-tensile tests have shown that lath martensite in fully martensitic steel in fact deforms in a highly anisotropic manner, showing large strains under favorable habit plane orientations. The question is whether this mechanism can also occur in dual-phase steels. Therefore, a range of novel methodologies have been developed for high-resolution and robust measurement, identification, and model validation of micromechanical deformation mechanisms. First, a new class of ’2D’ experiments is presented that enables one-to-one quantitative comparison between microstructure-resolved mechanics in experiments and simulations, by circumventing the notorious difficulty of dealing with an unknown 3D subsurface microstructure through a dedicated sample fabrication and testing routine of ’2D’ micrometer thin specimens and by discretization of the full 3D phase and grain geometry for advanced crystal plasticity modelling. Second, a novel nanomechanical testing and alignment framework, including a new nanoscale digital image correlation (DIC) patterning method, is introduced. Finally, the Slip System based Local Identification of Plasticity (SSLIP) method is presented to measure full-field crystallographic slip system activity maps from DIC data, which can directly be compared to numerical predictions. These methods have been applied to study lath martensite in DP steel in greater detail than before. It is shown, by a combination of ’1D’, ’2D’ and ’3D’ experiments and CP simulations, that strong anisotropic martensite plasticity, as previously observed in fully martensitic steel, also occurs in dual-phase steels due to the specific crystallography of the martensite islands. Moreover, it was found by detailed experimental-numerical comparison that the softer martensite plasticity mechanism that occurs over the habit plane also inhibits damage initiation in martensite notches.

ABSTRACT. The divertor, one of the main parts of the International Thermonuclear Experimental Reactor (ITER), extracts the heat and radiating species generated by the fusion reaction. The divertor contains various sub-assemblies, each comprising numerous components made of copper-chromium-zirconium (CuCrZr) cooling ducts which are joined to tungsten (W) monoblocks using a copper (Cu) interlayer. The W/Cu joint is paramount not only for efficient heat exhaustion but also for maintaining the structural integrity of the divertor under the extreme environmental conditions expected at ITER; thereby its assessment is crucial. It is in this regard that the present work aims to understand the mechanical behavior across W/Cu joints through FEM modeling of nanoindentation. A crystal plasticity model implemented a user-defined material law that allowed grain-scale FE modeling of the plastic strain field and lattice distortions expected after nanoindentation in the close vicinity of a W-Cu joint. The influence of the local lattice orientation and the proximity of the joint was investigated by comparing numerical predictions to experimental observations. The further simulation of heat cycles provides insights that could be useful for further assessment of ITER monoblocks.

ABSTRACT. In this study, uniaxial tensile tests and equi-biaxial Marciniak tests were carried out to identify the deformation modes and damage mechanisms of a ZnAlMg coating (5 wt%Al and < 1 wt%Mg) deposited on a sheet of S250GD grade structural steel. The microstructure of the coating consists of dendrites surrounded by binary and ternary eutectics. As with most ZnAlMg coatings, the formability and subsequent corrosion resistance of the coating is affected by the differences in mechanical properties of these microconstituents and the different crystal orientations of the grains. Mechanical testing was executed for monotonical loading and tests were interrupted at different levels of deformation. Local strain fields were calculated by digital image correlation and related to ex-situ crack distributions at the mesoscopic scale obtained by scanning electron microscope (SEM) imaging. SEM imaging and electron backscatter diffraction (EBSD) analyses showed that strain was mainly accommodated by twinning and slip in the zinc phase, leading to dynamic recrystallisation in some locations. Three main damage mechanisms were observed: cleavage in the zinc phase, decohesion at the interface of Al-Zn eutectoid globules and cracking in MgZn2 lamellae. These tests and observations were complemented by an in-situ SEM tensile test, to understand crack propagation and activation of plasticity better. Crystal plasticity finite element simulations were carried out for a coating/substrate system, where the coating was modelled as a polycristal with a single grain in the thickness direction. Three material behaviours were considered: one for the zinc dendrites, another for the mixture of eutectics and a macroscopic elastoviscoplastic behaviour for steel. Several features of the coating microstructure, such as dendrite/eutectic ratio, grain size and basal texture, were experimentally characterised by SEM analysis. Finally, calculated twinning and slip activities, and local strain and stress fields were compared with orientation maps and crack patterns observed in the experimental tests.

ABSTRACT. A combined experimental and simulation strategy is presented to evaluate the impact of slip transfer on the deformation mechanisms in pure Ti. From the experimental viewpoint, the 3D microstructural information was acquired by laboratory diffraction contrast tomography, and thus, all the parameters that characterize grain boundaries were available prior to deformation. Slip transfer across grain boundaries and the strain distribution after deformation were ascertained by means of high-resolution digital image correlation. Despite most of the grains following the usual geometrical slip transfer criteria, some atypical behaviors were observed, such as delayed slip transfer, partial slip transfer, and slip transfer involving poorly oriented slip systems triggered by the local stress state. Simultaneously, a representative volume element of the microstructure was generated from the 3D data, ensuring a direct correspondence between the model and microstructure. The mechanical behavior of the polycrystal was simulated using a dislocation-based crystal plasticity model that accounts for slip transfer/blocking, where the critical resolved shear stress was fitted for each slip system family. The analysis of the experiments alongside the numerical simulations provided a comprehensive understanding of the deformation mechanisms across grain boundaries in pure Ti.

ABSTRACT. This study investigates the deformation mechanisms of P91 martensitic steel at room temperature employing micropillar compression tests and crystal plasticity finite element (CPFE) modelling. The active slip systems were identified through micropillar compression tests, where micropillars were milled using a focused ion beam instrument. These micropillars were extracted from grains within the polycrystal P91 with different crystallographic orientations suited for activating various slip plane families in a body-centered cubic (BCC) structure. The CPFE model, describing the cumulative rate dependent behaviour of each slip system within the single crystal, was calibrated for each slip family through the stress-strain curves of the micropillar compression tests. The scanning electron microscopy (SEM) images of the deformed micropillars were compared with the corresponding prediction of the CPFE models to evaluate the predictive capacity of the finite element models. The accuracy of slip trace predictions, specifically regarding the angle of slip trace and shape of the deformed micropillars for {110}, {112}, and {123} slip plane families was verified.

ABSTRACT. Periodic metamaterials and architected materials have emerged as a powerful tool for, among others, controlling or suppressing elastic waves by bandgap engineering. However, the manufacturable design space extends far beyond periodic structures. Spatially graded architectures with smoothly varying unit cell designs have hardly been explored for wave manipulation but offer a rich playground for wave manipulation. We here present a combined experimental-computational study into this rich design space at the example of spatially graded truss lattices. We confirm experimentally that Bloch-Floquet theory is an accurate approximation, as long as the grading in unit cell design is smooth. We further introduce ray tracing for dispersive elastic media as a convenient numerical approach to predict and design wave motion in graded, elastic and dispersive media (by separating the small-scale unit cell design from the large-scale spatial variations in a homogenization step). Using an adjoint-based optimization scheme, we present examples of how design optimization can lead to interesting and peculiar wave motion in graded truss lattices, including wave focusing, frequency splitting, and the realization of complex wave trajectories.

ABSTRACT. The aim of the research is to investigate an impact of mass distribution on the plate surface to the dynamic properties and natural frequencies of the simple structural elements (plates). In the optimization process, a genetic algorithm was used. The authors attempt to optimize the arrangement of mass on the plate's surface to maximize the gaps between adjacent natural vibration frequencies. Problems related to structural dynamics were solved by FEM implementation into the algorithm. The research provides data on the correlation between the occurrence of bandgaps in frequencies and the mass distribution. The obtained results were analyzed and described in terms of plate’s dynamics properties after optimization process. The authors also demonstrate the validity of applying the described optimization tool to the presented problems.

ABSTRACT. Shell-based architected materials, as exemplified by spinodoid topologies, provide a practical solution to address the prevalent stress concentration issues observed at junctions in truss-based structures, which often result in a reduction in mechanical performance. Despite the proven effectiveness of these structures, their development spans a broad design space. To seamlessly integrate them into crash energy absorbers, optimising the pertinent parameters becomes crucial for enhancing crush efficiency and energy absorption. A comprehensive understanding of the structures' behaviour under compression requires the inclusion of plasticity and damage models within finite element models. However, such inclusions increase computational costs, making optimisation with high-fidelity methods a costly endeavour. As an alternative approach, employing a probabilistic method through Bayesian Optimization strategically reduces the number of evaluations of resource-intensive observations. Results indicate that this approach offers a computationally efficient means of optimising functions with limited datasets.

Moreover, mapping physical properties to microstructural topology space poses a challenge, as multiple topologies can yield the same effective properties. We have proposed an inverse-design method for designing architected materials with diverse physical properties. The results demonstrate its effectiveness in addressing permeability-diffusivity-mechanical synergy, expanding the tunable scope of multi-physical performances, and tailoring functionally graded metamaterials with desired multi-functionality.

ABSTRACT. Lattices emerged in recent decades as a promising class of architected materials with a vast design space. Many machine learning models have been proposed as surrogate to numerical modelling in predicting their mechanical properties for rapid design applications. However, they are often not scalable, lack the appropriate physical constraints and hence are limited to a small fragment of the vast design space. Here we develop a graph-based neural network to predict the fourth-order stiffness tensor of any arbitrary periodic lattice. We build upon the equivariant MACE model and introduce positive semi-definite constraints that ensure energy conservation. To train the model, we assembled a generalised dataset of over 1 million unit cells with arbitrary crystal symmetries, stretching, bending and mixed behaviour, and varying degrees of complexity with an average connectivity from 3 to 16 and with up to 150 nodes per unit cell. We demonstrate an example application of the model in structural optimization.

ABSTRACT. With the advancements in additive manufacturing, the fabrication of complex lattice structures has become possible. This has led to increased interest in architected materials featuring topologies based on Triply Periodic Minimal Surfaces (TPMS) due to their mathematically controlled geometries and excellent mechanical properties. Triplic Periodic Minimal Surfaces (TPMS) refer to a type of periodic implicit surface characterized by having zero mean curvature. In essence, these surfaces are locally minimizing the surface area for a specified boundary. A great number of TPMS have been identified. While ongoing efforts focus on characterizing individual TPMS topologies, the successful selection of these topologies for specific functions necessitates a general understanding of how geometric features influence mechanical behaviour. While most cellular structures are bending-dominated, stretching-dominated cellular structures present greater stiffness and strength than bending-dominated structures of the same relative density. Thus, it is of interest to identify stretching-dominated microstructures for lightweight structural applications. Currently, the Schwarz P topology stands out as the only identified stretching-dominated TPMS topology. This study explores the correlation between the crystallographic space group of the lattice and its deformation mode. The elastic properties of the Schwarz P, Neovious, P+C(P), OCTO, PJx and PPJPxxx-J, all belonging to the Pm3 ̅m space group, were obtained through finite element analysis with periodic boundary conditions. A linear correlation between the E modulus and the relative density has been found, suggesting stretching-dominated deformation. Simulations are complemented with experimental uniaxial compression tests.

ABSTRACT. Magnetorheological elastomers (MREs) are composite materials made of magnetizable particles embedded in a soft elastomer matrix. They belong to the class of smart materials since some of their properties, such as their stiffness, can be modified by the application of an external stimulus, a magnetic field in their case. In the presence of a magnetic field, they can also exhibit large deformations and/or displacements. Hence, they stand as promising candidates for numerous engineering applications linked to tunable damping, non-contact actuation, morphing surfaces or artificial muscles. The simplest form of MRE samples is isotropic due to a homogeneous dispersion of magnetizable spherical particles in their matrix but curing these composites under magnetic fields can impart them with anisotropic properties through the creation of particle chains in the direction of the curing field. In this work, the coupled magneto-mechanical behavior of both isotropic and anisotropic soft MREs is characterized experimentally and reveals that structural instabilities are ubiquitous in the samples. Such instabilities are further harnessed in model structures including an MRE thin film deposited on a soft non-magnetic substrate that can display reversible 2.5D wrinkles at its surface under coupled magneto-mechanical loading. The influence of the magneto-mechanical loading parameters on the morphology of the obtained wrinkles is analyzed and the prospect for transitioning from 2.5D patterns to 3D patterns is discussed.

ABSTRACT. The use of structural instabilities allows for swift responses triggered by mechanical force or specific displacement thresholds. The advent of responsive materials has facilitated the adaptation of such structural instabilities into actuators that promptly deform under external stimuli. Nevertheless, the rapid transitions between equilibrium states entail significant viscoelastic roles at the material level, influencing the structural behavior on a larger scale. Our study offers a comprehensive understanding of the impact of viscoelastic effects on bistable structural transitions, incorporating both a novel experimental perspective and a thorough modeling analysis. These findings are applied to magneto-responsive bistable structures, presenting a roadmap for designing effective actuation conditions. The bistable transition's functionality relies on the interplay between the magnetic field amplitude and application rate. The comprehension of viscoelastic and magneto-mechanical coupling enables efficient actuation through temporal magnetic pulses, eliminating the need for sustained magnetic fields. Ultimately, we integrate these insights to create a responsive structural component, enabling modulation of transient and steady bistable transitions based on the application rate of external magnetic stimuli.

ABSTRACT. study the behavior of magnetoactive elastomers (MAE) undergoing large deformations while exited by magnetic fields. We analyze the role of the microstructures in the overall performance and stability of the soft active composites. We examine the coupled behavior of the active composites with (i) periodically and (ii) randomly distributed active particles embedded in a soft matrix [1], and (iii) periodic laminate composites and anisotropically structured composites with chain-like structures [2-4]. We identify the key parameters governing the magneto-mechanical couplings. Moreover, we find advantageous microstructures that give rise to significant enhancement of the coupling and actuation of the active materials [1]. Furthermore, we show that even very similar microstructures, such as periodic composites with hexagonal and rectangular representative volume elements, exhibit very different behavior in terms of their actuation and effective properties [1]. Next, we investigate the coupled magneto-elastic instabilities MAE. These instabilities may occur at different length scales [3, 5], and, potentially, they may be exploited to achieve new functionalities such as tunable band-gaps [6-10]. We explore the role of external magnetic fields, microstructure parameters, and consentient properties on the multiscale instabilities.

REFERENCES:

[1] E. Galipaeu et al. Int. J. Solids. Struct. 51: 3012-3024, 2014 [2] S. Rudykh and K. Bertoldi. J. Mech. Phys. Solids. 61: 949-967, 2013 [3] P. Pathak et al. Int. J. Mech. Sciences, 213: 106862, 2022 [4] A. Goshkoderia and S. Rudykh. Composites Part B 128: 19-29, 2017 [5] A. Goshkoderia et al. Phys. Rev. Lett. 124: 158002, 2020 [6] N. Karami-Mohammadi et al. J. Appl. Mech 86: 111001, 2019. [7] Q. Zhang and S. Rudykh. Mechanics of Materials 169:104325, 2022 [8] Q. Zhang et al. Int. J. Solids. Struct , 112396, 2023 [9] Q. Zhang et al. Ext. Mech. Lett. 59, 101957, 2023 [10] Q. Zhang et al. Int. J. Solids. Struct 289, 112648, 2024

ABSTRACT. Magnetorheological elastomers (MRE) are composed of elastic matrices infused with magnetic particles, which exhibit adaptive reactions to external magnetic fields. These responses result in mechanical deformations and modifications of the magnetorheological characteristics. Recently, there has been growing interest in soft MREs, characterized by polymeric matrices and malleable magnetic fillers, due to their potential applications in soft robotics, biomedicine and industrial components [1]. In particular, these materials show increased toughness during the fracture process when subjected to magnetic field actuation, a phenomenon attributed to the intricate interactions between magnetic particles [2].

This study delves into a comprehensive examination of the inherent fracture behavior of soft MREs under the influence of magnetic fields. Taking advantage of phase-field fracture modeling [3], a powerful approach known for its fracture regularization and the absence of predefined fracture trajectories, we present a pioneering magnetomechanical fracture modeling framework. This framework allows us to examine the complex interactions between magnetism and mechanics, with particular focus on understanding fracture behavior. The results of this research promise to reveal new insights into the post-fracture magnetic characteristics of soft MREs, paving the way for advanced applications and breakthrough innovations in multifunctional materials.

[1] A.K. Bastola, M. Hossain, A review on magneto-mechanical characterizations of magnetorheological elastomers, Composites Part B: Engineering, 200:108348, 2020.

[2] M.A. Moreno-Mateos, M. Hossain, P. Steinmann, D. Garcia-Gonzalez, Hard magnetics in ultra-soft magnetorheological elastomers enhance fracture toughness and delay crack propagation, Journal of the Mechanics and Physics of Solids, 173:105232, 2023.

[3] C. Miehe, L.M. Schänzel, Phase field modeling of fracture in rubbery polymers. Part I: Finite elasticity coupled with brittle failure, Journal of the Mechanics and Physics of Solids, 65: 93-113, 2014.

ABSTRACT. Laser Powder Bed Fusion (LPBF, also known as SLM, Selective Laser Melting) is a well-known Additive Manufacturing technology, among the most studied in literature for metals and alloys. Advanced LPBF now includes the ability to vary the laser parameters during fabrication, to perform in situ laser heat treatments, and to mix different powders. These recent developments open the possibility of printing architected materials, for which properties vary in space.

In the present work, we demonstrate how microstructures in LPBF can be modulated by proper control of laser parameters and/or associated selective laser heat treatments, operating in the solid state. One example refers to phase transformations in Ti-6Al-4V, and to the effect of Fe addition through in situ alloying. Microstructure changes are shown to be accurately monitored through operando high energy X-Ray diffraction, and acoustic emission. A second example illustrates how multi-material printing can benefit from the combination of powders and metallic foils, when dealing with “non-weldable” materials. The related hybrid LPBF process shows clear advantages over the combination of different powders, due to reduced residual stresses and better control of the formation of brittle intermetallics.

ABSTRACT. The integration of additive manufacturing (AM) and architected lattice structures has sparked significant scientific interest and excitement in the materials field. This innovative approach allows for the creation of custom cellular metamaterial components, introducing a new realm of lightweight, functional, and efficient structures that hold the potential to revolutionize various industries, including biomedicine, aerospace, and energy production.

Despite remarkable progress in metal AM technology, there are still challenges related to the processing and manufacturability of lattice structures. Processing defects that emerge during manufacturing can have a profound impact on the mechanical behavior of cellular materials, and these effects are not yet fully understood. The dependencies of these defects on unit cell design and printing size remain unclear and usually overlooked during the component design phase.

This work aims to address these challenges by employing a comprehensive approach that combines mechanical experimentation, material characterization, and computational modeling across various scales relevant to the problem. The study uses Ti6Al4V as the base material and selective laser melting as the AM technology. Three different cellular designs and three distinct strut thicknesses are employed to investigate the influence of both cell geometry and strut thickness on the manufacturing accuracy and mechanical performance of cellular materials.

The assessment of manufacturing accuracy begins with 3D surface comparison using X-ray tomography. Subsequently, mechanical performance experiments are conducted on the cellular materials. Computational models are then employed to establish connections between cellular design, relative density, the occurrence of defects, geometrical deviations, and mechanical performance of the lattice structures.

The findings of this research underscore the critical importance of incorporating defects and manufacturing deviations into the metamaterial design process. By doing so, a more reliable mechanical framework for the design of metamaterial components has been achieved.

Grant PID2020-116440RA-I00 funded by MICIU/AEI/10.13039/501100011033.

ABSTRACT. Metallic metamaterials are engineered materials that exhibit unconventional desirable physical and mechanical properties such as low density, high specific strength, and stiffness, making them attractive materials in structural engineering applications. Their fabrication techniques have evolved over time with additive manufacturing (AM), specifically powder bed fusion techniques, facilitating their manufacturing with complex geometries and high accuracy. However, major challenges of these laser-based techniques include the high initial and running costs, limited to few specific alloys, and low building efficiency. The hybrid manufacturing approach combining additive manufacturing and casting, also known as AM-assisted casting or hybrid casting, can be an alternative for the production of metallic lattices and has great potential in reducing the cost associated with the manufacturing. In the current work, we investigate the microstructural attributes and effective mechanical response of architected materials manufactured through hybrid casting in a combined manner for the first time [1], [2]. Different metamaterial topologies are engineered, and their microstructural properties arising from the hybrid casting process are thoroughly assessed using Scanning Electron Microscopy and Computer Tomography methods. To provide quantitative insights into their effective mechanical performance, their static and impact responses are also investigated and compared thoroughly with PBF effective metamaterial attributes. Distinct elastic and post-elastic characteristics, along with failure modes, are identified and comprehensively evaluated. The present work provides benchmark results regarding the process-structure-property attributes of hybrid-manufacturing AlSi10Mg-based metamaterials. Overall, the current study has demonstrated an alternative approach to producing complex metallic lattice materials with the capability of scaling directly to other alloys beyond the ones investigated here.

ABSTRACT. The manufacturing of lattice structures using laser powder bed fusion (L-PBF) technology has not yet been explored for high-strength aluminum alloy 7075. The present study is part of a project aiming at additive manufacturing components combining high strength with reduced weight and exploring the possibility to combine with self-healing capabilities.

The possibility to build lattice structures has been demonstrated for two distinct design categories: triple periodic minimal surfaces (TPMS) and strut-based lattices. The strut size is varied. These intricate geometries, manufactured in aluminum 7075, represent a significant advancement in the additive manufacturing domain, particularly for applications requiring a balance of strength and lightness.

The specific process parameters and powder composition are optimized for L-PBF to produce these high strength lattice structures. The porosity level, mechanical properties of the new lattices are characterized microstructurally and mechanically. In particular, in-situ X-ray tomography compression testing with Digital Volume Correlation to track local strains is performed on the manufactured lattice structures.

The initial outcomes indicate a promising potential for the use of these lattice structures in high-performance applications. The novelty of the work lies not only in the material used but also in the potential for these structures to exhibit self-healing properties, a feature that could redefine durability and longevity in critical applications.

ABSTRACT. The present study explores the effect of mixing various lattice architectures on the mechanical behavior of selective laser melted (SLM) Inconel 718 strut-based lattices. As a first approximation, we have selected several lattice architectures (BCC, FCC, OT, and SC) to analyze how a meta-lattice with a mixture of them respond from the mechanical behavior point of view. We have employed two mixing strategies: one where the lattice architectures are randomly distributed in the meta-lattice, and other, by using special quasi-random structures (SQS) to maximize the mixing and homogeneity. The mixing was carried out considering binary, ternary and quaternary meta-lattices, corresponding to using two, three or four lattice architectures respectively. Pure bending and stretching dominated behavior are noticed in pure BCC and SC lattice respectively, whereas a peak after elastic region followed by bending dominated behavior is noticed in pure FCC and OT lattices. In all the mixed lattices, either pure bending or very small peak after elastic region followed by pure bending dominated behavior is noticed. The specific yield strength (normalized by relative lattice density) is high for OT (220 MPa) and low for BCC (63 MPa), whereas it is similar for FCC (158 MPa) and SC (160 MPa) lattices. The results indicate that the mixing of architectures offers generally better mechanical properties than the rule of mixture using the results of the pure individuals. Also, the SQS lattices show in general better mechanical properties than the random lattices. Importantly, some of the combined architecture lattices show improved yield strength and strength at 30% engineering strain compared to the original lattices. It is noticeable the effect of adding SC to other lattices, where a systematic improvement of mechanical properties is observed.

ABSTRACT. Many bees possess a tongue resembling a brush composed of a central rod (glossa) covered by elongated papillae which is dipped periodically into nectar to collect this primary source of energy. In vivo measurements show that the amount of nectar collected per lap remains essentially constant for sugar concentrations lower than 50% but drops significantly for a concentration around 70%. To understand this variation of the ingestion rate with the sugar content of nectar, we investigate the dynamics of fluid capture by Bombus terrestris as a model system. During the dipping process, the papillae, which initially adhere to the glossa, unfold when immersed in the nectar. Combining in vivo investigations, macroscopic experiments with flexible rods and an elasto-viscous theoretical model, we show that the capture mechanism is governed by the relaxation dynamics of the bent papillae, driven by their elastic recoil slowed down through viscous dissipation. At low sugar concentrations, the papillae completely open before the tongue retracts out of nectar and thus fully contribute to the fluid capture. In contrast, at larger concentrations corresponding to the drop in ingestion rate, the viscous dissipation strongly hinders the papillae opening, reducing considerably the amount of nectar captured. This study shows the crucial role of flexible papillae, whose aspect ratio determines the optimal nectar concentration, to understand quantitatively the capture of nectar by bees and how physics can shed some light on the degree of adaptation of a specific morphological trait.

ABSTRACT. Slender structures or those composed of soft materials typically exhibit low rigidity, responding to small external loads. Capillary forces, often overlooked at larger scales due to their perceived weakness compared to other effects, can play a crucial role in shaping slender structures and soft materials. Recent studies have highlighted diverse deformations induced by capillary forces, such as softening the sharp geometry of a soft substrate, bending and buckling of flexible fibers, and folding, wrapping, and wrinkling of thin sheets. Our study builds upon experimental observations of a nano-fibrous liquid-infused tissue. Under slight compression, it spontaneously develops wrinkles through elasto-capillarity effects. Upon further contraction, specific regions undergo substantial collapse, forming surface reservoirs that enhance the membrane's deformability. The remarkable deformability of this synthetic system closely resembles that of cell membranes, making it suitable for applications in stretchable electronics, smart textiles, and soft biomedical devices. To elucidate the underlying mechanism, we employ theoretical and numerical modeling. The system is simplified to a 2D scenario, featuring a thickness-neglected, inextensible membrane confined within a liquid layer of constant volume. The configuration of the membrane-liquid system under certain compression is framed as an optimization problem. After discretization, the nonlinear problem is solved using an open-source tool CasADi for nonlinear optimization. Numerical continuation aids in identifying solutions under greater compression, where analytical solutions become impractical due to nonlinearity. The model reveals homogeneous wrinkles with slight compression, aligning with experimental findings. As compression increases beyond a certain threshold, wrinkles localize at one specific spot on the membrane. This transition provides insights into experimental observations, prompting further investigations into the behavior of liquid-infused membranes.

ABSTRACT. We study the coalescence between two slender structures withdrawn quasi-statically or at finite velocity from a liquid bath. When partially immersed, the structures interact with each other through the capillary force induced by their menisci whose shape changes with the retraction speed. As the structures are removed from the bath, their dry length increases, and they become easier to bend until the capillary force is strong enough to trigger contact. Surprisingly, the structures snap to contact from a finite distance at a critical dry length. The transition to coalescence is thus subcritical and exhibits a large hysteresis loop between two stable states.

An analytical coalescence criterion is derived when the structures are withdrawn quasi-statically from the bath with a good agreement with experimental data for rods and lamellae.

In the case of two rods removed at finite velocity, the size of the menisci around them grows with the retraction speed and the capillary interaction increases. The rods coalesce then at a shorter dry length. We characterize the menisci growth as a function of the capillary number and show that the interaction between the structures is given by the static interaction with an effective surface tension increasing with the capillary number.

In the case of two lamellae, the flow created between them during their removal from a bath generates a positive pressure pushing them away before the capillary interaction can, in some cases, bring them into contact. To study this overpressure, rigid lamellae are used and the variation in height of the liquid column between them during the removal is characterized as a function of the system parameters. This ingredient can then be used to describe the complex motion of flexible lamellae during their withdrawal from a bath.

ABSTRACT. A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid and flat surface and the tip of an incoming projectile. Under the assumption of the mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. We will discuss the role of solid compressibility and elucidate why nearly-incompressible solids feature substantial "gliding" prior to contact at the transition between regimes, the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue also that the above timescale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

ABSTRACT. Nearly every machine built since the Industrial Revolution involves rotating elements (e.g., wheels, gears, fans, pumps, and turbines), which are so ubiquitous that they often go unnoticed. These rotating systems are affected by three fictitious forces: the (i) Centrifugal, (ii) Euler, and (iii) Coriolis forces (this latter can typically be neglected in many engineering systems). Despite rotodynamics being a mature field studying the mechanics of rotating systems, the effects of Euler forces, produced by changes in angular velocity, remain surprisingly understudied. Predictive rotodynamics models are developed to optimize performance and predict the onset of instabilities to avoid failure. We introduce "Gyrophilia'' as an alternative approach to harness the combination of Centrifugal and Euler forces for novel functional mechanisms in rotating systems with tunable, switchable, and programmable characteristics. We have built a fully automated experimental setup to study slender elastic beams in a rotating frame, allowing accurate control of the angular velocity and acceleration. With our apparatus, accompanied by a simplified elastica model, we investigate the (in)stability of slender elastic beams with different boundary conditions. Our results demonstrate large and tunable structural deformation, buckling, and snap-through of pre-arched beams. We envision utilizing bistable beams as mechanical switches actuated through the angular acceleration, whose response to the rotational loading can be tuned by imposing non-trivial boundary conditions (e.g., angled clamps, contact, etc). We can engineer mechanical systems comprising multiple bistable beams subject to differing boundary conditions such that each component responds differently to a given loading condition. We can then apply principles of mechanical logic to build mechanical circuits that can be programmed through an accurate control of the angular velocity. We demonstrate how such principles could be exploited to sequentially actuate three rotating bistable beams, which could act as a peristaltic pump in a centrifugal microfluidics cartridge.

ABSTRACT. DNA in viral capsids, plant leaves in buds, and geological folds are examples in nature of tightly packed low-dimensional objects. However, the general equations describing their deformations and stresses are challenging. We report experimental and theoretical results of a model configuration of compression of a confined elastic sheet, which can be conceptualized as a 1D line inside a 2D rectangular box. In this configuration, the two opposite ends of a planar sheet are pushed closer, while being confined in the orthogonal direction by two walls separated by a given gap. Similar compaction of sheets has been previously studied, and was shown to buckle into quasi-periodic motifs. In our experiments, we observed a new phenomenon, namely the spontaneous instability of the sheet, leading to localization into a single Yin-Yang pattern. The linearized Euler Elastica theory of elastic rods, together with global energy considerations, allow us to predict the symmetry breaking of the sheet in terms of the number of motifs, compression distance, and tangential force. Surprisingly, the appearance of the Yin-Yang pattern does not require friction, although it influences the threshold of the instability.

ABSTRACT. Brittle matrix-based composites generally exhibit damage due to microcracks growth when they are subjected to mechanical loadings. We aim at establishing a nonlinear homogenization model for composites with growing damage. To this end, we rely on an incremental variational homogenization approach available only for elasto(visco)plastic composites [5, 1, 6]. Following [5], we first introduce a linearization of the elastic-damageable laws of the phases. After implementing appropriate stationnarity conditions (see [2]), the resulting Linear Comparison Composite (LCC) is then homogenized by using Hashin- Shtrikman bounds. The incremental variational procedure is implemented for composites made up of linear elastic spherical particles embedded in a damageable matrix. In order to assess the model, we perform full-field (Finite Element) simulations on a 3D cell consisting of a damageable matrix containing a linear elastic spherical inclusion. A phase-field approach (see [3]) is used to predict the effective behavior of the composite, as well as the overall damage evolution. A full characterization of the local fields and their fluctuations are also provided (see detail in [2]). The numerical results provide a validation of the model, even the latter needs to be improved for a better account of the damage heterogeneity.

References [1] Agoras M., Avazmohammadi R., Ponte-Castaneda P., International Journ. Solids Struct., 97, 668–686, 2016. [2] Ben-El-Barguia G. An incremental variational approach and computational homogenization for composites with evolving damage, PhD, Sorbonne University, 2023. [3] Bourdin B., Francfort G.A., Marigo J.J., Journal of the Mechanics and Physics of Solids, 48, 797-826, 2000. [4] Fantoni F. et al., A phase field approach for damage propagation in periodic microstructured materials. Int. Journal of Fracture, 223, 53–76, 2020. [5] Lahellec N., Suquet P., J. Mech. and Phys. of Sol, 55, 1932–1963, 2007. [6] Lucchetta A. et al., Int. Jour. of Solids and Structures, 158, 243–267, 2018.

ABSTRACT. Metallic cellular materials are of interest in numerous engineering applications as they combine low density with attractive features of metals (e.g., ductility and strength). Today, these materials are routinely used (e.g., in structures that absorb mechanical energy, or as biomedical scaffolds and heat exchangers). To reveal their potential in novel emerging applications (e.g., as battery electrodes), a fine understanding of their mechanical deformation and failure is instrumental.

In this work, the tensile response is investigated experimentally for AlSi10Mg cellular materials produced by laser powder-bed fusion (LPBF). Specifically, the metamaterials of this study have a porous architecture in which pores, of arbitrary elliptical shape, are randomly-dispersed in the Al-alloy matrix. Their porous mesostructure is first generated numerically by means of a random sequential absorption algorithm [1], and then fabricated by LPBF additive manufacturing. Using FE-based Digital Image Correlation (DIC) [2] with mesoscale meshes consistent with the pore distribution combined with X-Ray tomography, the mesoscale damage mechanisms underlying tensile deformation is quantified for this class of cellular solids. It is shown that the latter combine features of ductile fracture of metals with the defect-sensitivity typical of cellular metals produced by additive manufacturing.

[1] Hoosmand-Ahoor et al. Mechanics of Materials 173 (2022): 104432. [2] Hild et al. Experimental Mechanics 61.2 (2021): 431-443.

ABSTRACT. The biomedical community faces significant challenges regarding aneurysm rupture. Aneurysm growth is linked to the degeneration of the aortic wall and collagen, where, over time, certain collagen fibres may rupture. Consequently, the orientation of micro-cracks resulting from collagen rupture can influence the progression of the damage. This study investigates the damage initiation at the crack tip under uniaxial loading perpendicular to the crack. The analysis is done with numerical simulations using a user subroutine in ABAQUS, based on the Gasser–Ogden–Holzapfel (GOH) model for anisotropic tissue. This study will help to predict the critical crack orientation for the aneurysm rupture.

ABSTRACT. The influence of plasticity on high-temperature stress-assisted grain boundary oxidation of nickel-based superalloys used in applications such as turbine rotor discs is investigated using the method of Discrete Dislocation Plasticity (DDP). The misfit stress fields of triangular and nib-shaped intrusions are represented by a continuous distribution of edge dislocations whose extra half planes give the volumetric misfit of the oxide, which is implemented in a planar formulation of DDP by invoking the linear superposition principle. Volumetric misfit of an intrusion several microns in length generates high stresses in the parent material, which in turn leads to the nucleation of dislocation that are driven by the applied stress to the intrusion interface. Pile-up stresses on the order of 1 GPa cause localised growth and morphology change of the intrusion by stress-assisted diffusion. The analysis of the intrusion stress reveals that the morphology change relaxes the compressive stress inside the intrusion near its base, which increases its effective fracture resistance. Numerical experiments also show that an applied tensile stress increases the growth rate of the intrusion in defect-free samples, whereas in pre-strained samples it is found that dislocation pile-ups ahead of the oxide reduce the intrusion growth rate. This finding provides the first mechanistic explanation for reconciling an inconsistency in key experimental findings in the literature, which respectively identify a tendency for shorter and longer intrusions in samples subject to an applied load.

ABSTRACT. Although it is well known that local contamination can accelerate the initiation and propagation of cracks, it is not well understood the role of the morphology of the contamination pattern. Indeed, most experimental approaches deposit layers of contaminants without understanding the experimental epistemic uncertainty of this approach. This work integrates models and experiments to explor the cracking of Ni base single crystal superalloys induced by salt under sulphur environments at moderate temperatures. A phase field model is implemented to understand the interaction of multiple cracks arising from the contaminant while C-ring and fatigue tests were employed to validate the analysis. The results demonstrate that multiple nucleation of cracks can be avoided by reducing the size of the contaminant. As a result, crack shielding and coalescence can be prevented, which has a significant impact on damage, including ten times longer cracks and half the fatigue life.

ABSTRACT. It is impossible to underestimate the importance of hydrogen, especially renewable hydrogen, in the energy transition. Despite the huge potential and rising demand for renewable hydrogen, there are significant challenges that need to be overcome. One specific problem is the use of metallic equipment for high-pressure hydrogen gas applications (pressure vessels, transport networks...). These components are susceptible to hydrogen embrittlement, a phenomenon that can lead to structural degradation and severe damage. The effects of hydrogen embrittlement present a significant risk since they may shorten the life of these structures and affect their reliability and security. Therefore, the development of a numerical model to validate the design of hydrogen related systems is critical for addressing the massive industrial challenge and scientific obstacle. In this context, this study consists in developing a finite element (FE) model based on the phase field theory for hydrogen assisted fatigue. The phase field theory has recently gained a big popularity in the scientific community due to its ability to model initiation and propagation of cracks and to facilitate the integration of complex physics. In this work, the phase field theory was extended to model hydrogen embrittlement and fatigue. The FE tool thus developed integrates both mechanical modeling of the stress and strain fields, phase field modeling of damage and cracking, and modeling of the local hydrogen concentration and its evolution. Knowing that the mechanical response of the structure is sensitive to the hydrogen pressure and the loading frequency applied, different cases of applications were investigated by varying these two parameters at room temperature. Moreover, the model was employed to capture crack interaction with other defects. In this presentation, these different aspects of the FE model will be detailed as well as the different case studies that will demonstrate the capabilities of the FE simulation tool.

ABSTRACT. Liquid metal embrittlement (LME) refers to the reduction in ductility and toughness of a solid metal when in contact with liquid metals. This kind of material property degeneration poses a serious challenge for several industrial sectors, including the automotive industry, in which the embrittlement of advanced high-strength steels by their liquified Zn coating during welding is of major concern. This makes Fe in contact with liquid Zn a highly relevant example of an LME-susceptible metal couple.

To aid the elucidation of the atomic-scale origins of LME, we established an atomistic simulation framework, which offers sufficient versatility for the assessment of general grain and phase boundaries. This framework takes the form of a K-controlled molecular dynamics (K-test) setup for interfacial cracks. The simulation domain is confined to the area of interest regarding LME, i.e. the near-crack tip region, and can be constructed using anisotropic linear elasticity theory. Thereby, the employment of the Stroh formalism allows accounting for cracks along the boundaries of arbitrarily oriented dissimilar anisotropic materials.

The second crucial ingredient for accurate and reliable predictions of material properties using molecular dynamics approaches is the choice of a suitable interatomic potential (IAP) that describes the interaction between the system’s atoms. Since there is no such potential for the Fe-Zn system yet, we are developing a new machine-learning IAP to this end. Therefore, atomic cluster expansion (ACE) potentials are employed, since they feature a superior combination of accuracy and evaluation speed. The three main stages of the development process are the establishment of a suitable database, containing all relevant atomic configurations, the training procedure and the testing and validation of the obtained IAP. These stages are discussed, as well as obtained results. Finally, the application of the overall framework for the investigation of LME at the atomic scale is discussed.

ABSTRACT. We aim at investigating the full coupling between gradient damage, poroelasticity and fluid flow phenomena in saturated porous media. To this end, we first extend the thermodynamics-based Biot-Coussy theory of porolelasticity in order to incorporate gradient damage processes. Inspired by Stainier 2013 (Adv. App. Meca., Vol 46, P. 69-126) in thermomechanics, we introduce the concept of kinetic porosity that allows to well clarify the interaction between skeleton deformation and fluid filtration in the connected pore space, this extension is then implemented to establish an incremental variational formulation expressed as a four-field minimization problem of an incremental total energy functional, which incorporates poroelastic energy, as well as the dissipation related to damage evolution and fluid flow in time increment. Moreover, by taking advantage of a suitable approximation of the kinetic porosity in the current time increment, the above mentioned minimization problem is reduced to a three-fields dependent one, involving the displacement and damage fields of the skeleton phase as well as the fluid pressure field, which is shown to result in the equilibrium state of the saturated porous media. An incremental variational principle is thus established (Zhang 2023, Ph.D. thesis, Univ. Lorraine). Subsequently, a variational model for the fully coupled problem is consistently proposed and is numerically implemented by means of a semi-staggered optimization algorithm. This procedure is applied in a benchmark modeling for which relevant solutions and numerical results related to hydraulic fracturing are available. The model is also employed for the evaluation of an Excavation Damage Zone (EDZ) around a waste storage underground gallery. The model is shown to be able to deliver sufficiently reliable predictions, which extends either in presence of coupled poroelastic effects or for pure elastic-damage couplings.

ABSTRACT. The present talk deals with the effect of acid aqueous environment on the fatigue lifetime of Short Fiber Reinforced Thermoplastics (SFRP) employed for automotive components. In this context, two polyamides (PA6 and PA66) containing 35% weight ratio of short glass fibers were aged for 1000h at pH=2,5 and T=60°C and compared with unaged materials. At first, the effects of chemical pre-aging was characterized from Scanning Electronic Microscopy and Differential Scanning Calorimetry and then the monotonic tensile properties were studied. The results showed a slight embrittlement of the aged materials and no stiffening, consistently with the molecular chain breakage due to hydrolysis and with the unaffected crystallinity ratio. Fibers were debonded from the matrix on an outer layer of 200 µm thickness. Then, stress-controlled uniaxial fatigue tests were performed at constant amplitude, frequency (1Hz) and load ratio (R=0.1) for three orientations (0°, 45° and 90°) with respect to the injection direction. An in-situ device was specifically developed to test immersed samples in acid solution, with the challenge to ensure stability and homogeneity of the solution and of the strain measurement all along fatigue tests. A slight decrease of fatigue lifetime was evidenced for pre-aged samples, especially when fibers were mainly aligned with the tensile direction (0°). Such decrease was not observed in samples aged and tested in water.

ABSTRACT. We introduce a comprehensive mixed-mode stress analysis conducted on a thick composite tidal blade featuring a strategically positioned hole with notches. Tidal blades, crucial components of stream turbines, experience complex loading conditions due to dynamic tidal forces. A mixed-mode analysis approach considering all fundamental modes of crack opening (Mode I, Mode II, and Mode III), is employed to capture the full spectrum of stress states around the notched hole. Here, we revisit existing fracture criteria for 2D and 3D mixed mode loading to evaluate their performance compared to the recorded measurements. A digital image correlation (DIC) method is additionally used to correlate the strain field surrounding the geometric discontinuity. Furthermore, a finite element analysis (FEA) model is validated against the experimental data and various loading scenarios are simulated, including tidal forces, wave-induced vibrations, and fatigue loading. The effects of the hole and the direction of the notches are systematically investigated to assess their impact on stress concentration and crack propagation. This research contributes an understanding of the mechanical behaviour of thick composites under mixed-mode loading, offering valuable insights for the design and modelling stages of composite tidal turbine blades.

ABSTRACT. Testing in the Very High Cycle Fatigue (VHCF) regime comes with a number of difficulties that lead to a lack of research, resulting in conservative designs of wind turbine and helicopter rotor blades. With low loads and up to 108 load cycles, small variations of test parameters can have a huge impact. This study investigates the effect of pure tensile loading compared to four-point bending fatigue, both with a stress ratio of R = 0.1. Two test series with a (902/02)s and a (90/0)2s cross-ply lay-up made of glass fibres and epoxy resin are tested at four load levels. The bending tests are conducted on a special VHCF test rig, to overcome typical problems such as long testing times, specimen heating and self-fatigue of the test equipment. In addition to the in-situ flexural modulus recorded by the test system, the crack density and the delamination area ratio are determined from transmitted light photographs automatically taken throughout the test. The tensile tests are performed on a hydraulic testing machine, to archive the high loads required. To avoid fatigue damage to the hydraulic test machine, the majority of the tests are stopped after the first cracks appear. Only two specimens per test series are tested up to 108 load cycles. Therefore, this study focuses on the comparison of first damage, such as crack initiation, on the experimental side. Further investigations of the crack growth and delamination growth tendencies are conducted with numerical simulations using a parametric FE model. The evaluation of the experimental data shows higher fatigue limits under four-point bending fatigue. The numerical simulations indicate a higher tendency for delamination growth under pure tensile loading. This is supported by the stronger delamination growth on tensile specimens observed in the experimental data.

ABSTRACT. Isotactic polypropylene is one of the most used semi-crystalline polymers due to its low cost, ease of processing and versatile mechanical properties. In long-term applications, one of the key properties is the resistance against fatigue crack propagation (FCP), i.e. the resistance to the growth of small initial flaws that ultimately trigger failure. The resistance against FCP in polypropylene is, however, not systematically studied in literature or well understood. Therefore, in this study, we present an overview of the FCP in polypropylene as a function of both temperature and molecular weight and relate the observed performance to the local fibril deformation mechanisms active at the crack tip. To measure the FCP, Compact Tension samples were combined with an image acquisition setup to measure the crack length in-situ over time. From the measured crack length a, the stress intensity factor K_I and the crack growth rate da/dt are determined. Combined these give the crack growth kinetics described by a Paris law; and are defined by a pre-factor A and slope m according to: da/dt=A⋅(K_I⋅(a))^m. Experiments conducted over a range of temperatures reveal that the slope m varies with temperature which has not been observed for, e.g., polyethylene. Additional experiments conducted at different frequencies and load ratios show that at high temperatures the FCP is insensitive to frequency and decelerates with decreasing load ratio, suggesting a fibril disentanglement mechanism is dominant, whereas at low temperatures the FCP becomes frequency dependent and accelerates with decreasing load ratio, suggesting a fibril buckling mechanism becoming dominant. The transition between these two mechanisms depends on the molecular weight of the material. Remarkably, temperature superposition can be successfully applied to the range of molecular weights. These observations enable us to uniquely model the FCP behaviour in polypropylene as a function of molecular weight, temperature, load ratio and frequency.

ABSTRACT. Recent work on elastomer fatigue shows that it is still difficult to establish the link between lifetimes measured on laboratory specimens and the lifetimes of real parts. In particular, it is difficult to predict the effect of complex loadings on a part whose geometry is itself complex. We propose to present recently developed tools to help make this transition from laboratory to in-service behavior.

Based on theoretical work that defines locally the multiaxiality of a deformation state, and on finite element simulations, we propose a method for constructing fatigue test campaigns that are representative of real-life stresses. This method uses finite elements to explore distortion modes within the material and their intensity, in order to reproduce them in the laboratory. Through this method, we propose to link the local state in the sense of continuum mechanics to the control of a tension-torsion machine.

ABSTRACT. Rubber blends are ubiquitous in countless technological applications. More often than not, rubber blends exhibit complex interpenetrating microstructures, which are thought to have a significant impact on their resulting macroscopic mechanical properties. In this talk, as a first step to understand this potential impact, I will present a bottom-up or homogenization study of the nonlinear elastic response of the prominent class of bicontinuous rubber blends, that is, blends made of two immiscible constituents or phases segregated into an interpenetrating network of two separate but fully continuous domains that are perfectly bonded to one another. The focus will be on blends that are isotropic and that contain an equal volume fraction (50/50) of each phase. The microstructures of these blends are idealized as microstructures generated by level cuts of Gaussian random fields that are suitably constrained to be periodic so as to allow for the construction of unit cells over which periodic homogenization can be carried out. The homogenized or macroscopic elastic response of such blends will be determined both numerically via finite elements and analytically via a nonlinear comparison medium method. The numerical approach makes use of a novel meshing scheme that leads to conforming and periodic simplicial meshes starting from a voxelized representation of the microstructures. In will present results for the fundamental case when both rubber phases are Neo-Hookean, as well as when they exhibit non-Gaussian elasticity. Remarkably, irrespective of the elastic behavior of the phases, the results will show that the homogenized response of the blends is largely insensitive to the specific morphologies of the phases.

ABSTRACT. Additive manufacturing (AM) allows for the design of complex-shape components with multifunctional properties, as conductive polymeric composites. Depending on the nature of the polymeric matrix, such multifunctional materials can be printed via Fused Filament Fabrication (FFF, for thermoplastic polymers) or via Direct Ink Writing (DIW, for elastomeric polymers). The microstructural multi-physical interdependencies that occur at a material level are still an open question. In this work, we conduct a multi-physics characterisation of 3D printed polylactic acid (PLA) and PDMS materials doped with Carbon Black (CB) nanoparticles through combined electrical, thermal and mechanical tests. In addition, a full-field homogenisation approach was employed to model the multi-physical interdependencies that appear at a microstructural level.

From an experimental perspective, we tackle the problematic by performing tests where pairs of physics were isolated. In this regard, three different sets of experiments were performed: i) electro-thermal; ii) thermo-mechanical; and iii) mechano-electrical. Finally, a thermo-electro-mechanical test was performed, considering all the variables simultaneously. For the modelling approach, full-field homogenisation techniques are employed to simulate the interdependencies observed in our experimental campaign. The governing equations of the problem are solved in a Representative Volume Element (RVE) of the composite. The problem domain accounts for three phases: i) polymeric matrix; ii) CB particles; and iii) microscopic voids.

The results obtained in this work show the strong interplays that are highly nonlinear under large deformations. Additionally, we prove that our in-silico methodology has a great potential for conductive filament manufacturers to optimize the multifunctional material properties and scale them to the structural scale. As future work, we finally provide evidence of incorporating hard-magnetic properties within the soft materials to enable self-healing capabilities on top of the electro-mechanical behaviour.

ABSTRACT. Recently, the progress in additive manufacturing led to the design of a new class of artificial materials with complex inner architectures that characterized by mechanical attributes that are commonly cannot be found in natural engineering materials. The present work focuses on a numerical study of thermomechanical effective properties as well as the strain gradient field of materials with uniform and graded inner architectures. The effective property calculation is based on numerical implementation for the solution of thermoelasticity equations on a predefined Representative Volume Element (RVE), employing the appropriate periodic boundary conditions. Using the field (temperature, displacement) and flux field (heat flux, traction) calculations, the effective values of Young modulus, shear modulus, thermal conductivity, thermal expansion and Poisson ratio are estimated by computing the corresponding average quantities. A parametric study is conducted considering inner architecture designs based on Gielis' formula and different combinations of base materials and Volume fractions. Then, a Neural Network (NN) model capable of predicting the effective properties for several combinations of inner architecture designs, base material properties and volume fraction is constructed and trained with the obtained numerical results. Finally, the developed numerical formulation is employed for the thermoelastic strain gradient field calculation on architected materials occurring from thermal and mechanical loads.

ABSTRACT. Previous studies have shown that thermodynamic topology optimization (TTO) is an variational optimization approach that can also be used for hyperelastic components. Large deformations offer the opportunity, for example, to integrate the function of a hinge or a joint in just a single component. Accordingly, the TTO provides promising potential in terms of sustainability. However, the severe non-linearities due to the large deformations setting are the source of manifold numerical challenges that need efficiently to be counteracted to enable TTO applicable for industrially relevant optimization problems.

In the current contribution, we investigate the update of the TTO in connection with the update of the displacement field in large detail to discover an ideal update procedure for the staggered solving of the two coupled partial differential equations (displacements and density variable). For this purpose, the optimization is carried out at different stages of the numerical solution process (time steps) leading to different time integration schemes. The effect of these variants is examined in terms of their achieved optimization and computational performance. Along with theoretical basis we present various numerical results.

ABSTRACT. The endothelium is the biomaterial lining the luminal surface of blood vessels and is undergoing significant stretch in cardiovascular physiology and pathology. Using custom stretch devices and protocols, we challenged young and aged/senescent endothelial monolayers with a range of physiological and supraphysiological deformations in vitro. The results show that upon acute high-rate stretch endothelial monolayers developed prominent damage, visible as intercellular and intracellular void formation. For all cells, damage increased proportionally to level of stretch applied, but damage extent depended on cell phenotypes. The subsequent response to after acute stretch determined the partial death and detachment of senescent and aged endothelial cells from the substrate, while the young counterpart rapidly restored the monolayer integrity. Similarly, we observed higher fragility of senescent cells when subjected to physiological levels of cyclic stretch stimulation. In order to rationalize the experimental observations we developed a computational model representing endothelial cells as discrete networks of cytoskeletal components. Adapted to the different cell populations, the model predicted differences in stretch induced mechanical loading of stress fibers and cell-cell junctions, pointing at the more affine deformation of the senescent monolayer as the main factor causing the observed damage. Based on the results of the model, we biochemically decreased the adhesion to the substrate of the senescent monolayers, in order to reduce their affine deformation. This was sufficient to dampen the stretch-induced damage, thus confirming model predictions. Overall, our results show that young endothelia are more resilient to stretch, and that the fragility of senescent monolayers is associated with their stronger adhesion to the substrate. This result is intriguing and may open new avenues for reducing the risk of barrier impairment in aged blood vessels.

ABSTRACT. In this work, we present an in-silico model that combines continuous convection-diffusion-reaction model and agent-based model to predict atheroma plaque growth. We explore how hemodynamics affect the mechanics and transport properties in the arterial wall, triggering cellular events that are related to atheroma plaque growth. The hybrid model has three modules coupled together: computational fluid dynamics (CFD), continuous module of continuous convection-reaction-diffusion (CRD) equations and agent-based model (ABM). The cellular processes included in the model are: mitosis and apoptosis of the cells; production and degradation of the extracellular matrix; production, phagocytosis and necrosis of macrophages, becoming foam cells (FCs) due to excess LDL in the wall; and the change of phenotype of smooth muscle cells (SMCs) from contractile to synthetic. Based on the results obtained in the continuous analysis for WSS and oxLDL concentration, atheroma plaque growth was reproduced in the ABM model. The transfer of information from the ABM to the continuous model was performed by segmentation of the output image provided by the ABM. The ABM shows the evolution of the atheroma plaque after 30 years, reproducing greater growth in the areas with higher concentrations of WSS and oxLDL.

ABSTRACT. The management of thoracic aortic aneurysm patients involves stratifying the risk of dissection and rupture using diameter measurements. Traditional guidelines group patients into categories based on known syndromic pathologies (Marfan, Turners, Ehlers-Danlos) and sporadic (acquired) groups based on aortic valve type (tricuspid or bicuspid). Aortic diameter alone is a poor predictor of aortic tissue integrity.

I will present the results of machine learning models of the patient characteristics from the McGill University Health Centre Aortic Clinic. Patient information was collected from the clinic cohort (146 patients) along with ex vivo planar biaxial tensile properties of resected tissue, genetic screening, in vivo strain imaging to better understand our patient population profiles and ability to predict biomechanical function. Supervised machine learning algorithms provided good estimates of ex vivo biomechanics based on clinically based metrics. Moreover, an unsupervised model demonstrated TAA patients cluster into unique and reproducible clinical subgroups with distinct biomechanical profiles and aneurysm geometry.

ABSTRACT. Laser-based Powder Bed Fusion (LPBF) of ceramics enables the fabrication of objects with complex three-dimensional shapes otherwise challenging or even impossible to produce with conventional manufacturing routes. However, the mechanical properties of LPBF-manufactured ceramics components are poor due to a large number of structural defects. Often, such defects are investigated by X-ray computed tomography. This allows studying in 3D the density and shape of pores and cracks in printed samples. Dynamic processes can be studied by fast in situ X-ray radiography, however, this method lacks 3D information.

In this work, we present the first results obtained by operando tomographic microscopy during LPBF of magnetite-modified alumina. This new technique allows tracking the 3D microstructural evolution during printing with a time resolution of 10ms. The experiments are performed at the TOMCAT beamline of the Swiss Light Source with an LPBF setup with a green laser. The effect of laser energy density on surface roughness, powder denudation zone and porosity formation mechanisms is investigated. Higher power results in a significant increase in the melt pool width, but not in its depth and no melt pool depression is observed. For the investigated ceramic system, the forces due to the recoil pressure do not significantly influence the melt pool dynamics. Increasing power allows for avoiding lack of fusion porosity, but enhances the formation of spherical porosity that is formed by either reaching the boiling point of liquid alumina or by introducing gas bubbles by injection of hollow powder particles into the liquid. The acquired information, not only provides an understanding of underlying processes but also is crucial for the development and verification of models used for the LPBF process simulations.

ABSTRACT. Crystal lattice defects can dramatically alter material properties and functionality. Furthermore, defects energy and mobility in nano-objects vary significantly from their bulk counterpart. Thus, the understanding of defects behavior is crucial to optimize material performance. Bragg coherent X-ray diffraction imaging (BCDI), a lensless imaging technique that relies on phase retrieval algorithms, allows for 3D characterization of morphology and strain with a 3D spatial resolution of 10 nm and picometer sensitivity of lattice displacement field. It has emerged nowadays as a revolutionary tool to image defects and strain fields in 3D. BCDI is thus an ideal technique to probe the stability of defects in nanocrystals during mechanical straining.

Here, we report three-dimensional defect characterization at the onset of plasticity in a 550 nm Pt nanoparticle from two recent successive synchrotron experiments: The first at ESRF-ID01 and the second at SOLEIL-CRISTAL. The former is an experiment that combines in-situ mechanical testing using a custom-built atomic force microscope with BCDI. The three-dimensional reconstructions from the Pt 111 coherent diffraction patterns show the nucleation of prismatic dislocation loops during indentation. The elastic field measured inside the crystal during indentation estimates that the shear stress required to generate defects is 6.4 GPa, which represents the upper theoretical limit of elasticity and is unprecedented for Pt nanoparticles.

In the latter experiment at the SOLEIL synchrotron, the complete dislocation network was imaged post-mortem and the Burgers vector for each dislocation line was determined by multi-reflection BCDI (Pt 111, Pt 002, Pt 020, and Pt 002 Bragg peaks) revealing sessile dislocations.

ABSTRACT. MATEIS Laboratory has developed the concept of a new microCT platform designed, developed and manufactured by RX Solutions. The DTHE, stating for Double Tomograph for High Energy, covers some of the lab scale current challenges. This “out of catalogue” unique piece of equipment is designed around one rotation axis and two strictly identical 300 kV Xray lines. The platform is dedicated to large samples and/or highly absorbent materials. It allows microCT scans using a spot size ranging from 4 μm to few hundreds of microns, with simultaneous or sequential acquisition, with identical or distinct resolution, with identical or distinct energy, with or without external sollicitation, etc... This presentation will first quickly describe the equipment and then show some examples of first results of in situ experiments in different scientific domains where the capabilities of the equipement is used to improve acquisition speed or image quality.

ABSTRACT. Recent studies demonstrating amorphization of olivine under high-stress have raised interest in the mechanical properties of amorphous olivine (a-olivine) [1, 2]. In this study we investigate the mechanical properties of amorphous olivine deformed at room temperature either ex situ by nanoindentation, or in situ in a TEM under uniaxial tension using a Push-to-Pull (PTP) device. Thin films of a-olivine were deposited by pulsed laser deposition (PLD). In nanoindentation, a-olivine a-olivine exhibit a viscoelastic-viscoplastic behavior without fracture. Long-term relaxation tests show a strain-rate sensitivity m∼0. 05 [3]. Under uniaxial tension in situ in the TEM, a-olivine deforms plastically but with a gradual transition that makes impossible the determination of a precise threshold. The strength attains values up to 2.5 GPa. The fracture strain reaches values close to 30 % without e-beam irradiation. Under electron illumination at 200 kV, the strength is lower, around 1.7 GPa while higher elongations close to 36 % are obtained. Alternating beam-off and beam-on sequences lead to exceptionally large fracture strains equal to 68 % at 200 kV and 139 % at 80 kV. EELS measurements were performed to characterize the interaction between the electron beam and a-olivine. At a voltage of 80 kV, radiolysis accompanied by oxygen release dominates whereas at high voltage the interaction is dominated by knock-on type defects. Radiolysis is also the dominant interaction mechanism at 200 kV with low exposition which corresponds to most of our deformation experiments.

[1] K. Kranjc et al. (2020). Amorphization and plasticity of olivine during low‐temperature micropillar deformation experiments. Journal of Geophysical Research: Solid Earth, 125, e2019JB019242.

[2] V. Samae et al. (2021) Stress-induced amorphization triggers deformation in the lithospheric mantle. Nature 591, 82–86.

[3] P. Baral et al. (2021) Rheology of amorphous olivine thin films characterized by nanoindentation. Acta Materialia, 219, 117257.

ABSTRACT. Hybrid nanolaminates (NLs) consisting of alternating layers of metal and metal oxide exhibit excellent mechanical properties and resistance to irradiation damage, which are critical for various structural and functional applications. The strength and ductility of NLs very much depend on layer thicknesses and interfacial characteristics. Investigations by in situ nanomechanical testing in a transmission electron microscope (TEM) are extremely valuable in relating the mechanisms of deformation and failure to microstructural evolutions within individual layers as well as at the interfaces. In addition, the influence of the electron beam irradiation (EBI) must be assessed to evaluate possible artifacts but also to enlarge the range of test conditions.

Here, we address Al/Al2O3/Al tri-layer model systems involving two amorphous/crystal interfaces that exhibit enhanced ductility over 50% with a high ultimate tensile strength above 1550 MPa under uniaxial tension. The extreme plasticity results from the time-dependent viscoplastic response under low-strain rate (10-6 s-1) deformation which is very much controlled by EBI. The influence of EBI on the stress-strain behavior was systematically confirmed by switching on and off the electron beam which led to drastic changes in the mechanical response. The microstructure of the NL deformed under beam-on was characterized by significant delocalization of the plasticity. Intriguingly, both Al-layers exhibited localized necking at the majority of grain boundaries (GBs). This suggests that GB diffusion creep is the dominant mechanism operating at low-strain rates and this feature did not manifest itself in samples deformed at higher strain rates or in the absence of EBI. Furthermore, the localized plasticity at GBs is associated with GB migration which we have analyzed in our study based on the novel combination of nanoscale digital image correlation (DIC) with nanomechanical testing inside TEM. The role of the crystal/amorphous interface and the transmission of plasticity at this interface is also discussed.

ABSTRACT. Oxide inclusions in the SiO2 – Al2O3 – MnO pseudo-ternary system are precipitated within iron by in-situ reaction, analyzed for their composition and characterised by means of micromechanical tests that give their intrinsic, in-situ mechanical properties such as their hardness and their stiffness, or the strength of their interface with the iron-based matrix. Preliminary results suggest that adjusting the MnO content of the resulting oxides inclusions can be used to obtain an inclusion stiffness close to that of the iron matrix, thus reducing the elastic inclusion/matrix mismatch in steel and making MnO-rich inclusion compositions attractive candidates if one seeks to minimize local stress concentrations in the alloy under mechanical loading.

ABSTRACT. Modern functional oxides are mainly tailored by doping, namely, by changing the defect chemistry, which is essentially the studies of point defects and their interactions in solid state. On the other hand, in recent years, dislocations as line defects have been shown to improve the mechanical and functional properties of a fraction of advanced oxides for promising applications such as actuators and sensors. This poses an increasing demand to understand the interaction of dislocations and point defects in functional oxides. Here, we report the influence of doping on the mechanical response of single-crystal strontium titanate using nanoindentation tests. By using the Berkovich and 2 µm spherical indenter tips, we observe the changes in the pop-in event which is reflected in the maximum shear stresses for dislocation nucleation, as well as the nanoindentation creep rate. The possible contributing factors: cation (Sr,Ti/Nb) and anion (O) vacancies, doping elements and lattice distortion induced by dopant elements are discussed, and the lattice frictional stress is estimated based on the dislocation etch pits. The nanoindentation results are further linked with the bulk plastic deformation behavior of the doped and undoped samples. The current results shed new light on the interaction between dislocations and point defects, which appear to strongly impact the dislocation nucleation, multiplication and mobility, hence the room-temperature plasticity of strontium titanate.

ABSTRACT. High-temperature nanoindentation analysis is challenging due to instrument-related artifacts such as thermal drift and frame stiffness. Here, we investigated the impact of frame stiffness and thermal drift on the apparent mechanical properties by comparing the results of static nanoindentation experiments at different temperatures. The indents were analyzed using the Oliver-Pharr method, while two different load profiles were applied. Additionally, automatic image recognition (AIR) of the micrographs of the indents as well as statistical methods, i.e., correlation heatmap and p-value evaluation, were employed to understand the instrument-related artifacts. The tested materials include ferritic, martensitic, and austenitic steels as well as a Ni-based alloy for high-temperature applications.

The thermal drift analysis showed significant drift at 400 °C, which then decreased at 600 °C. Frame stiffness varied considerably for different temperatures, showing an inverse correlation with thermal drift. Both the Oliver-Pharr method and AIR revealed a hardness decrease of the materials with increasing temperature. As expected, AIR demonstrated less susceptibility to thermal drift. The heatmap correlation and p-value evaluation of the hardness with respect to the materials’ chemical compositions indicated that Cr and Ni positively influence the hardness resulting in improved hardness with increasing temperatures. The combination of the two analysis methods yields reliable mechanical properties despite the significant fluctuations in thermal drift and frame stiffness for different temperatures.

ABSTRACT. Chemical degradation of polymeric materials results in a deterioration of mechanical properties, which limits the serviceability of polymer products. To unravel the molecular processes at the origin of this degradation, molecular simulation can be employed. However, the timescales of chemical reactions leading to polymer degradation are typically beyond what can be reached with conventional molecular dynamics (MD) simulations. To retain molecular detail in combination with the ability to reach long timescales, so-called network dynamics has been developed [1-4]. This approach focusses exclusively on local minima in the free-energy landscape and transitions between them via saddle points – with corresponding energy barriers – to describe the long-time dynamics, including chemical reactions. At the core of the network-dynamics approach is an efficient numerical procedure to – departing from local minima – establish nearby saddle-points and then in turn find other connected local minima, without the need for the full dynamics. After discussing the main principles of this simulation strategy, initial results for the chemical degradation of polystyrene in the glassy state will be presented. For the latter, we use both reactive force-fields (ReaxFF) [5] as well as density-functional theory (DFT) simulations to study the reaction pathways and energy barriers, which will eventually be used in the network dynamics.

Acknowledgment: Part of this research forms part of the research program of DPI, projects #745ft14, #820, and #829.

[1] GC Boulougouris, DN Theodorou, J. Chem. Phys., 2007, 127, 084903. https://doi.org/10.1063/1.2753153 [2] GG Vogiatzis, LCA van Breemen, M Hütter, DN Theodorou, Mol. Syst. Des. Eng., 2023, 8, 1013. https://doi.org/10.1039/D2ME00256F [3] GG Vogiatzis, LCA van Breemen, M Hütter, J. Phys. Chem. B 2021, 125, 7273. https://doi.org/10.1021/acs.jpcb.1c02618 [4] GG Vogiatzis, LCA van Breemen, M Hütter, J. Phys. Chem. B 2022, 126, 7731. https://doi.org/10.1021/acs.jpcb.2c04199 [5] W Zhang, ACT van Duin, J. Phys. Chem. B 2018, 122, 4083. https://doi.org/10.1021/acs.jpcb.8b01127

ABSTRACT. Fiber-reinforced polymer composites have gained popularity due to their high specific mechanical properties and lightweight construction, leading to greater industrial scrap production. The recycling of CFRPs is encouraged by the European Parliament's Directive 2008/98/EC. The recycling process begins with the shredding of scraps, followed by the compression molding of the resulting small flakes. Predicting the mechanical properties of recycled composites accurately is challenging due to their heterogeneous structure, which includes flakes and resin with different mechanical properties. This complexity makes modeling with mono-scale numerical methods difficult. This study employs a multiscale technique to investigate the complex mechanical properties of recycled composites. The numerical model includes micro-level interactions (fibers in thermoplastic matrices), meso-level components (loaded chips and resin), and macro-level analyses, providing a comprehensive understanding of material behavior. At the meso-level, the detailed geometric model in finite element analysis is critical for accurately predicting the mechanical properties of recycled composites. This includes in-plane and out-of-plane orientations, resin-rich areas, and interactions among flakes. The primary objective is to establish a predictive model for the mechanical properties of recycled fiber-reinforced composites using voxel-based approach. Flake generation through the random sequential adsorption (RSA) algorithm, subdivision into sub-cubes, and a sinking process based on finding neighbor process ensures essential geometrical features such as out-of-plane orientation and resin-rich areas. Cohesive zone modeling defines interactions between flakes, with assigned material properties for Carbon/ Poly-ether-ether-ketone (C/PEEK) and PEEK in flakes and resin-rich areas, respectively. Validation, based on microscopic images, confirms the accuracy of the geometrical model. The consistent alignment between mechanical test results and simulation outcomes reinforces the reliability of our predictive model. This study provides a big step forward in our understanding and prediction abilities in recycling composite materials.

ABSTRACT. In response to the growing demand for efficient materials in modern technology, elastomer-based composites have emerged as high-performance engineering materials. The description of the finite deformations in elastomers typically involves formulations based on strain rates and the application of the finite element method (FEM) and homogenisation for elastomer-based composites with the assumption of effective material properties. However, using FEM, especially in composite materials, usually is a trade-off between accuracy and computational speed. Therefore, developing novel approaches is essential for predicting elastomer composites’ mechanical behaviour without extensive experimental trials. In this context, the comprehensive homogenisation approach for elastomer-based composite materials explores the interaction between a hyperelastic matrix and a linear elastic filler in a carbon black-reinforced S-SBR composite. The framework helps to optimise the manufacturing process for nano-filler-reinforced elastomer-based composites, allowing a quantitative assessment of the impact of both the matrix and the filler on the final material properties and applying strain energy functions for describing the mechanical behaviour of the composite components. On the mesoscale, a unit cell of the material is proposed for the first iteration that considers the fractal dimension of the filler structure, defining volume fractions for the filler, matrix, and interphase. This enables the use of the rule of mixture, summing the strain energy required to predict the deformation in the composite. The work provides a comprehensive perspective on the suggested homogenisation and demonstrates the potential of the strain-energy-based homogenisation approach for elastomer-based composites.

ABSTRACT. In this study, for a complex-shaped carbon-fiber-reinforced plastic (CFRP), machine learning model is used to predict the three-dimensional information of defects from the sum of principal stresses at the surface (DSPSS) calculated from the finite element method (FEM). The reason for using DSPSS in this study is that it is intended to perform inverse estimation of defects using infrared stress measurements. CFRP specimens are made in different microstructure and the way of lamination. Here, a prosthetic leg with a curved surface is used as the analysis model. A CFRP prosthetic leg is characterized by the lamination of prepregs with multiple microstructures, such as plain weave, twill weave, and unidirectional in practical use. CFRP prosthetic leg models which have different microstructures and the way of lamination are created in FEM, and homogenized finite element analysis is conducted to obtain DSPSS. In the process of prediction, the predictabilities of internal defects for each model are compared, and differences among microstructures are discussed using microstructural features and stress distributions. A graph neural network is used to predict the three-dimensional structure of the defects inside the prosthetic leg based on DSPSS of the prosthetic leg analyzed by FEM. As an adaptation, this machine learning model can be used in the experimental data.

ABSTRACT. This study presents an RBF-based surrogate computational homogenization for viscoplastic composites. Recently, several surrogate models and data-driven methods have been developed to replace the classical constitutive model for history-dependent materials, such as elastoplastic and viscoplastic materials, with the help of mechanistic machine learning techniques (MMLT). Meanwhile, the application of MMLT to multi-scale problems has also been studied in order to reduce computational costs for micro-macro coupled two-scale analyses. However, to the best of our knowledge, most of those studies employ neural networks, in which the regression processes are black box-like in terms of mechanism. Against this issue, we proposed to extensively utilize radial basis function (RBF) interpolation to create a surrogate model that can be a substitute for the microscopic simulation in the two-scale analysis of viscoplastic composites. The macroscopic stress is represented by the surrogate model in consideration of the dependencies on strain rate and temperature. Also, thanks to the simplicity of RBF interpolation, we can easily understand how the macroscopic stress is regressed. The capability of the present method is demonstrated through numerical examples. First, by conducting numerical material tests (NMTs) on a representative volume element (RVE) consisting of multiple viscoplastic materials, we obtain a data set representing the macroscopic constitutive relationships for various deformation patterns. Second, a surrogate model is created by applying RBF interpolation with the data set. Third, for validation purposes, the responses of the surrogate model are compared with the results of NMT that has been performed with unseen loading and temperature histories. Finally, a macroscopic analysis is performed as online computation, followed by the localization analysis. The resulting macroscopic and microscopic responses are compared with the results of direct numerical simulations to demonstrate the validity of the present methodology.

ABSTRACT. Crystal plasticity takes into account the crystal lattice and the corresponding slip systems that are characteristic of the underlying crystalline microstructure. The mechanical behavior of polycrystals is significantly affected by grain boundaries (GBs), which are considered as material singular surfaces in classical continuum mechanics [1]. Simulating the evolution of microstructure can be challenging and costly from a numerical perspective when tracking sharp interface (SI) grain boundaries (GBs). To avoid this issue, the CP can be implemented in the multiphase-field approach (MPFM) as suggested by [2]. Modeling surfaces as diffuse interfaces with finite thickness, the MPFM is an efficient method for treating evolving surfaces. In this talk, we provide a concise overview of how crystal plasticity is applied within the diffuse interface region [4] using the jump condition approach [3]. The consistency between the MPFM and SI solutions in a bicrystal is demonstrated through three-dimensional simulations. Additionally, the evolution of the polycrystalline microstructures following elastoplastic deformation are examined as an initial step towards the modeling recrystallization processes [5].

REFERENCES

[1] A. Prahs, T. Böhlke, Contin. Mech. Thermodyn, Vol. 32, 1417–1434, 2019.

[2] B. Nestler and H. Garcke and B. Stinner, Physical Review E, Vol. 71, No. 4, pp. 041609 1–6, 2005

[3] D. Schneider, F. Schwab. E. Schoof, A. Reiter, C. Herrmann, M. Selzer, T. Böhlke, B. Nestler, Comput. Mech., Vol. 60 (2), 203–217, 2017.

[4] A. Prahs, L. Schöller, F. Schwab, D. Schneider, T. Böhlke, B. Nestler, Comput. Mech., DOI: https://doi.org/10.1007/s00466-023-02389-6, 2023.

[5] T. Kannenberg, L. Schöller, A. Prahs, D. Schneider, B. Nestler, Comput. Mech., DOI: https://doi.org/10.1007/s00466-023-02423-7, 2023.

ABSTRACT. Deformation twinning is a prevalent inelastic deformation mechanism in certain metals and alloys. Modeling twinning poses additional challenges in comparison to plastic slip due to the critical dissimilarities in the underlying mechanisms and characteristics. In this study, a finite-strain model of coupled twinning and plastic slip is formulated by combining the phase-field method and crystal plasticity. A distinctive aspect of the model lies in its treatment of deformation twinning as a displacive transformation (as in martensitic phase transformation), and thus the related kinematics is characterized by a volume-preserving stretch and a rigid-body rotation, rather than a simple shear as in the classical approach. The stretch-based kinematics is particularly relevant when conjugate twinning systems are crystallographically equivalent.

Spatially-resolved evolution of twin microstructure under nano-indentation is studied for an Mg alloy with an HCP crystal structure. To this end, a two-dimensional finite-element-based computational model is developed that includes one twin deformation variant, i.e., two conjugate twinning systems, and three effective slip systems (one basal and two pyramidal slip systems). The simulation results reveal several interesting effects, including an intriguing branched microstructure and pop-in events. A detailed analysis is conducted regarding the sensitivity of the twin microstructure and load-indentation depth on the lattice orientation and indenter radius (size effects).

ABSTRACT. The microstructure of materials has a tremendous influence on their macroscopic properties, which naturally leads to seeking to tailor microstructures to reach wanted features. In the case of metals, it has been long recognized that grain boundaries control the macroscopic mechanical properties. Thus, the optimization of macroscopic properties through the design of grain boundaries has naturally grown over the years. Controlling the grain features at will requires a thorough understanding of the physical and mechanical phenomena occurring during thermomechanical processes, especially the phenomenon of recrystallization. Recrystallization can be roughly said to be composed of two steps: (i) nucleation and (ii) growth of the newly nucleated grains. While grain growth can be relatively well modelled, nucleation is still a challenging topic. The Kobayashi-Warren-Carter (KWC) phase field model is thought to be able to naturally account for such phenomena. It has been extended recently by Ask et al. in a new model with full coupling for material and lattice rotations, which also accounts for the evolution of dislocation densities. In this work, we aim at illustrating the capabilities of the modelling framework to handle grain nucleation occurring during recrystallization. Hence, we will consider conditions generating high lattice curvatures and stored energies such as slip or kink bands that are likely to promote nucleation of new grains. Thus, using a a three-dimensional version of the coupled model proposed by Ask et al., simple loading cases, such as torsion, will be tested on single and polycrystals to trigger grain nucleation.

ABSTRACT. One of the main limitations of phase field-based models is their high computational cost. Within the framework of finite elements, the size of the finite elements must be orders of magnitude smaller than the scale factor responsible for regularizing the diffuse field. This requirement necessitates many elements to capture the interface or discontinuity. Additionally, the solution exhibits a strong dependence on the orientation of the elements. In order to reduce the computational cost and improve the convergence rate of the solution, a non-conforming finite elements formulation is presented. This formulation enriches the Galerkin solution space with non-conforming functions, including incompatible bubbles. All of this is carried out within a consistent variational formulation. The developed formulation demonstrates better convergence errors than the standard formulation and reduces the influence of the element's orientation. The application of this formulation is proposed for phase-field fracture models.

ABSTRACT. Transformation plasticity refers to the anomalous average strain observed when steels undergo solid-state phase transformations under applied loads. This phenomenon has gained widespread attention due to its significant impact on various industrial fabrication and forming processes, including heat treatment, welding, run-out table processes, and coiling. Several analytical macroscopic models, based on idealized microstructures and strong assumptions, have been proposed. However, a common limitation of these models is their linearity (or weak non-linearity) concerning applied stress, making them suitable only for small loadings. Experimental evidence suggests that the transformation plastic strain becomes highly non-linear with increasing applied stress. Additionally, analytical models often exhibit a logarithmic behavior as a function of product phase proportion, a trend not consistently confirmed by experiments, especially in cases of diffusion-controlled transformations.

As a result, comprehensive full-field simulations of polycrystals have been conducted to enhance our understanding of transformation plasticity. These simulations typically use fast Fourier transform (FFT) algorithms on periodic microstructures, focusing solely on volume expansion due to phase transformation. In this contribution, full-field FFT simulations incorporating visco-plasticity (Chaboche law) and the complete eigenstrain associated with the austenite-to-ferrite phase transformation (e.g., Bain strain) at high-temperature conditions (750°C) are performed with variations in grain distributions, grain orientations, precipitate locations, and applied stresses. The dual objective is to gain deeper insights into the detailed mechanisms responsible for non-linearity with respect to applied stress and the evolution of average plastic strain concerning product phase proportion and to establish a computation database to develop a statistical macroscopic model. This model would incorporate, as input parameters, not only applied stress and product phase proportion but also the average strain rate governed by viscoplastic effects.

ABSTRACT. Bioabsorbable Mg alloys are currently being considered for biomedical devices that gradually disappear with time and neither hinder the growth of natural tissue nor require a second surgery for removal. Degradation of bioabsorbable materials should take place at a speed compatible with the growth of natural tissue and is important to develop simulation tools to assess the evo-lution of the corrosion over time and the corresponding degradation in mechanical properties. Mg corrosion in a chlorine solution was simulated using a phase-field model that incorporates both the anodic and cathodic reactions as well as the formation and dissolution of a Mg(OH)2 passivation layer, together with the role of mechanical stresses in accelerating corrosion kinetics. To this end, the free energy functional includes the chemical, electrical, gradient and mechanical energy contributions and the motion of the solid/liquid interface is governed by the electrochem-ical reaction at the interface, following the Allen-Cahn equation. Moreover, the transport of ionic species in the electrolyte and within the passivation film follows the mass balance law, while the formation and passivation of the passivation film is also considered. The model is validated against experimental results of corrosion Mg wires in fluids with different pH and chlorine ion contents, showing the potential of this strategy to assess the degradation of Mg devices in bio-logical fluids.

ABSTRACT. Rubber-like materials make up key components in a wide variety of engineering applications, ranging from replacement heart valves and soft robotics to O-rings in rocket stages. In many applications, rubbers are subjected to complex, non-proportional loading histories and exhibit the Mullins effect, a stress softening phenomenon where the apparent material stiffness in a given direction drops with stretching in the same direction. The Mullins effect is highly anisotropic - softening in one direction under uniaxial tension causes negligible softening in the orthogonal directions. Computationally efficient models for this effect are essential for the design of rubber components.

To this end, we present a model for the Mullins effect with a particular focus on the development of mechanical anisotropy. We maintain the micromechanical picture of rubber elasticity (where the rubber network is broken down into the behaviour of its constituent chains) and incorporate damage at the level of the individual chain. A tensorial description of the damage distribution is introduced from which the driving force for damage is identified. Anisotropic evolution laws for the damage distribution reminiscent of kinematic hardening in the theory of plasticity are then presented in both a damage function formulation and a variational formulation, ensuring thermodynamic consistency and enabling calculation of the consistent material tangent for finite element implementation. The model is verified against experimental data for homogenous deformations with changes in stretching direction. The model is implemented in the commercial finite element software ABAQUS as a user subroutine and simulations of complex loading are presented.

ABSTRACT. The thermomechanical behavior of natural rubber (NR) and butadiene rubber (BR) blends is explored in this study, focusing on an in-depth examination of nonlinear viscoelasticity, in particular the Payne and preload effects, and the integration of finite element analysis. A comprehensive theoretical framework is developed to capture the intricate interplay of these factors, providing a description of the mechanical responses of NR-BR blends under varying thermomechanical conditions. Experimental investigations complement the theoretical modeling with dynamic mechanical analysis (DMA) and uniaxial tensile testing to unveil the material properties of NR-BR blends. The experimental data help to validate and improve the theoretical model, reinforcing the correlation between the theoretical predictions and observed behavior. The model is implemented in a user material subroutine (UMAT) to employ finite element analysis (FEA) in ABAQUS to simulate and predict the macroscopic behavior of NR-BR blends, offering insights into the material performance under diverse loading scenarios and geometric configurations. By incorporating FEA with both experimental and theoretical results, our study improves the current state-of-the-art in terms of integrality and accuracy. The insights gained from this research are a first step in guiding the design and engineering of new self-healing rubber formulations with targeted applications in the automotive and aerospace industries.

ABSTRACT. Elastomers are typically modelled under the assumption of material incompressibility. Performing simple tension and bulk tests, we show that some class of elastomers can experience significant volume changes when large deformations are involved. The volumetric strain energy density (SED) functions available in literature exhibit limitations in modeling the large volumetric deformations of elastomers. Therefore, we propose a new volumetric SED which is capable of: (1) accurately describe the response of rubbers for both small and large volumetric deformations; (2) reproduce different behaviors for volume shrinkage and volume expansion; (3) adapt to other compressible materials, such as soft tissues, foams and gels. Following the deviatoric–volumetric split of the strain energy function, the Yeoh-Fleming hyperelastic model is chosen as deviatoric part for the proposed SED. An overall fitting to the experimental data from simple tension and bulk tests is carried out to calibrate the parameters of the combined SED. The results prove the effectiveness of the combined SED in modeling the response of elastomers under both shape and volume deformations. The proposed SED can be implemented in numerical codes to solve more complex problems involving compressible materials.

ABSTRACT. In finite torsion of cylinder a huge number of non-linear complex effects occur: contraction of the radius, elongation of the cylinder, arising of axial force, and the onset of instability are fascinating effects induced by the fully non-linear context. However, there is no trace in the literature of an exhaustive and complete work which fully investigates each case of torsion from a theoretical and experimental standpoint. Different cases of torsion are accounted for in the framework of non-linear elasticity: free torsion and restrained torsion. For these cases of torsion, experiments are very rare in the literature for soft materials as they require extremely sophisticated devices for the measurement of displacement fields and forces. Moreover, the case of pure torsion, which leads to a fundamental universal relation of solid mechanics, was never investigated in terms of the reliability of its fundamental assumptions. We present a new set of experiments on the free torsion and restrained torsion of polyurethanes and silicon rubbers. Along with the torsion tests, uniaxial tests of the rubber are presented. Based on the experiments and universal relation of pure torsion, we experimentally proof the relevance of the second invariant of deformation. We point out that the relevance of the second deformation invariant decreases as the deformation increases. Characterization of the materials, by means of the best fit procedure of the experiments, shows how much the simultaneous fitting of multiple states of stress can reduce the quality of the fitting. Among the energy forms here considered, both incompressible and compressible, we show that only the compressible energy law can grasp the experimental Poynting elongation of the rubbers. In addition to the above, we propose a new formulation in non-linear elasticity to predict the onset of instability in the case of restrained torsion.

ABSTRACT. The tire's structure architecture incorporates several composite plies of polymer cables within an elastomer matrix. The manufacturing process of these textile cables makes them complex mechanical objects. Hundreds of textile filaments of 10 to 30 µm diameter are assembled to form one or more filament bundles yarns. Then the filament bundles are twisted together to form a twisted cable. The resulting twisted cables undergo several chemical and thermal treatments to reach the final state. Textile cables are designed to support tensile stress in the rubber matrix to perform this function. Yet, due to the relatively specific arrangement of the plies, combined with certain conditions of tire use, the cables are also subjected to axial compression. Therefore, there is a need to quantify and understand the effect of this stress on cables in tires.

This study consists in evaluating the contribution of textile cables to the overall stiffness of the rubber/textile cable composite in compression, determining the critical points of damage to cables in compression by analysis of deformation mechanisms and finally, providing elements to feed numerical models for finite element simulation.

To assess the contribution of textile cable to the overall compressive stiffness of the elastomer/textile cable composite, an experimental protocol for compression testing on elastomer/textile cable composite has been set up. It considers the sample geometry, sample fabrication and test parameters required to achieve the conditions for a compression test. Initial test results show that the contribution of textile cables to the overall compressive stiffness of the composite depends on the stiffness of the elastomer in which the cable is immersed. The stiffer the elastomer, the greater the cable's contribution to the composite's overall compressive stiffness. Additionally, compression tests were carried out in-situ in a laboratory tomograph to study cable deformation mechanisms.

ABSTRACT. In this work, we have studied the mechanics of interfacial fracture in co-consolidated thermoplastic joints with and without crack stoppers subjected to quasi-static and fatigue loading by experiments and numerical models. We have performed quasi-static and fatigue tests on double-cantilever beam (DCB), end-notch flexure (ENF), single-lap shear (SLS) and crack-lap shear (CLS) coupons and on a mono-stringer sub-element. Also, we have developed two numerical models based on the cohesive zone modeling (CZM) method. The first model utilizes a modified tri-linear traction separation law, which is built by superimposing the bi-linear behaviors of the matrix and fibers, to simulate the mixed-mode fracture of co-consolidated thermoplastic joints by considering fiber bridging and the second model utilizes a modified bi-linear traction separation law to simulate fatigue interfacial crack growth of co-consolidated thermoplastic joints for any I+II mode-mixity ratio, requiring only pure mode I and II loading data as input. The models were fed and successfully validated by experimental data and then used to numerically design two crack stoppers, namely the Friction Stir Spot Welding (RFSSW) and the Induction Low Stir Friction Riveting (ILSFSR) crack stoppers, which were applied on the CLS coupons and the sub-element. It was found that both crack stoppers are capable of delaying the interfacial crack growth for the fatigue loading. The methods and findings of the present work show a great potential for use in the design of thermoplastic aerostructures assembled by co-consolidation or welding and can be proved very useful in the development of digital twins and in the digital certification process.

ABSTRACT. Dry forming is an emerging technology in paper packaging production. In contrast to traditional papermaking techniques, the pulp fibres are dispersed in air instead of water. Because of the low water content, the material only has to be pressed and heated during a short amount of time. In consequence, the process has shorter lead times and significantly lowered energy consumption. However, water is an important factor in traditional paper making, as it highly contributes to the molecular interactions that create the fibre-fibre joints, which in turn hold the fibre network together. In the absence of water, these interactions will be much weaker, resulting in a substantially different material behaviour. The work presented here is a characterisation of the dry-formed material, where mechanical testing has been carried out in different loading modes. The most important modes of loading, based on what the material experiences in the forming process, were chosen as in-plane tension, out-of-plane compression, out-of-plane shear, and, additionally, combinations of these. Materials in the whole density range were considered, from uncompressed fluff pads, to fully formed sheets, at various densities. The results show similarities to conventional paper materials, although the dry-formed materials are in all cases weaker than wet-formed counterparts. As mentioned before, this is attributed to decreased fibre-fibre joint strength. From the experimental outcome, simple relations for some of the investigated mechanical properties versus density are proposed. In future work, the aim is to create a complete material model, which can be used to simulate the full forming process.

ABSTRACT. Composite materials are increasingly preferred for various structural applications due to their numerous advantages. However, most structures undergo complex loading, resulting in a multi-axial stress state within the material. Estimating material properties under biaxial loading is a complex process. The planar biaxial testing technique proves highly accurate for biaxial mechanical properties compared to other out-of-plane methods. Although planar biaxial tests precisely predict material deformation behavior, their applicability is confined to the design of cruciform specimens. Improper cruciform specimen design causes non-uniform strain distribution, leading to failure outside the gauge region. The present study aims to design a novel cruciform specimen to achieve uniform strain distribution and failure within the gauge region. An optimized cruciform biaxial specimen is initially developed using a commercial finite element method. Four cruciform geometries (A, B, C, and D) undergo systematic analysis through finite element simulations. Geometry D, featuring a square slot, is the most suitable for biaxial testing. Carbon fiber reinforced polymer composites (CFRP) are utilized in the study, manufactured through the resin transfer molding (RTM) process. Strain evolution during planar biaxial testing is recorded using the Digital Image Correlation method. Experimental biaxial tensile testing of the proposed cruciform design verifies the effectiveness of the optimized parameters, with digital image correlation revealing maximum and uniform strain distribution in the gauge region. The stress-strain curve shows linearity for equi-biaxial loading, with a failure strain of 0.55%. Fracture analysis confirms fiber fracture and fiber pull-out as observed failure mechanisms.

ABSTRACT. Microstructures with bimodal and lamellar morphologies were prepared by heat treatment of titanium Ti-6Al-4V alloy at various temperatures. The electron backscatter diffraction (EBSD) analysis confirmed that the width of basal/{0001} macrozone reduces with increased heat treatment temperature. These samples were then subjected to tensile and interrupted strain-controlled low-cycle fatigue tests till a maximum of 200 cycles. The tensile response of bimodal microstructures was inferior compared to the lamellar microstructure. The energy dispersive spectrometry study revealed the alloying element partitioning phenomenon as a significant factor influencing tensile strength. Further, the total elongation is strongly dependent on the effective grain size. When subjected to the low cycle fatigue tests, bimodal microstructures also showed a large degree of cyclic softening. However, the lamellar samples failed at a significantly less number of cycles with limited cycling softening. EBSD study after 50, 100, and 200 cycles indicates a limited variation in the texture of the material. Chaboche isotropic-kinematic hardening model was implemented in Abaqus to predict the cyclic stress-strain response for bimodal and lamellar structures. Isotropic hardening parameters were calibrated based on the variation in cyclic yield strength (CYS) and cyclic stress amplitude (CSA). The stress-strain response predicted using the variation in CYS for bimodal microstructures was relatively accurate. However, for the lamellar microstructures, the preferable method of material parameter calibration was utilising the variation in CSA.

ABSTRACT. The plasticity criterion has been shown to strongly influence the global behavior of a rotating aeronautical turbine disk and its expected burst speed. Moreover, yield surfaces can evolve very rapidly with plastic strain. Their accurate knowledge is thus essential to precisely predict the behavior of a part subjected to multiaxial and non-proportional loadings such as the turbine disk. The use of polycrystalline plasticity models allows the numerical reproduction of yield surface distortion effects observed experimentally for all loading paths thanks to the model's proximity to the physical mechanisms at the origin of the plasticity.

In this study, experiments were conducted on a flat notched sample loaded in tension designed to enhance the effects of chosen plasticity parameters on the stress redistribution and strain development in the sample. Field measurement techniques were then used to compute the experimental fields throughout the loading and measure the boundary conditions to use in the simulations to better suit the experiment. This allowed the experimental fields to be compared to those predicted by finite element simulations of the sample carried out using Zset software. Two material behavior laws were identified on previous test results and used in this study : one model uses Hosford’s macroscopic phenomenological plasticity criterion whereas the second model is a simple polycrystalline model. Then, finite element model updating is performed to enhance the identification of material parameters. Finally, the strain localization during finite element simulations of the sample is studied in order to investigate the influence of numerical and material parameters on the global stress/strain curve and on the geometric properties of localization.

ABSTRACT. The development of new advanced steels, with a proper combination of mechanical properties, is supported to a wide extent by the design of microstructures consisting of a mixture of retained austenite and martensite/bainitic ferrite/proeutectoid ferrite. In this scenario, the exploitation of the transformation-induced plasticity (TRIP) phenomenon is key, which can be achieved by controlling the stability of retained austenite. Crystal plasticity has proven to be a useful tool for the identification of critical stress/strain conditions in complex polycrystalline microstructures. In the case of islands or blocks of retained austenite embedded in a matrix of either proeutectoid ferrite, dual-phase models based on crystal plasticity are well established. For more complex cases, such as microstructures where austenite islands are surrounded by bainitic blocks containing both film-like retained austenite and bainitic ferrite, simplified crystal-plasticity approaches might be wished. For that purpose, morphological, crystallographic and chemical factors, contributing to the strength of the bainitic microconstituent and constraining the deformation, need to be considered. In this work, DAMASK, a unified multi-physics crystal plasticity simulation package [1], is used to simulate the stress/strain response preceding mechanically-induced martensitic transformation in complex advanced steels containing retained austenite embedded in ferritic matrix. The microstructural models and simulations are experimentally informed with data from X-Ray Diffraction, nanoindentation and scanning electron microscopy. Acknowledgments: We express our gratitude to Carlos Garcia-Mateo and José Antonio Jiménez for the fruitful discussions. Special thanks to Radhakanta Rana (Tata Steel) for providing the material and engaging in insightful dialogues. Erick Cordova-Tapia and Lucia Morales-Rivas acknowledge CSIC for an iMOVE grant (Ref. IMOVE23203).

1.Roters, F. et al. DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science 158, 420–478 (2019).

ABSTRACT. The observation of deformation heterogeneities within polycrystalline materials has encouraged the development of mechanical models of crystal plasticity (CP), taking into account the local characteristics of the microstructure [1]. Usually, the comparison between simulations run with CP models and experimental results are carried out by focusing on effective responses. However, more local data can enrich the experimental database, using electron diffraction for surface data [2] or X-Ray diffraction for volume data [3]. Obtaining highly resolved experimental fields, witnessing the deformation of polycrystalline materials, opens the way to a fullfield confrontation, with CP simulations.

Diffraction Contrast Tomography allows the mapping of the microstructure, in terms of grains morphology and orientation at resolutions (few hundreds of nanometres) and over thicknesses (few hundreds of micrometres) unachievable by more conventional techniques. This way, a 3D description of the microstructure can be used as input for CP simulations with FFT-based methods, for computational efficiency purposes.

The implemented methodology offers the opportunity to perform identification for CP laws, using a Machine Learning-based approach and a multiscale and multimodal experimental database.

REFERENCES [1] Meric, L., Poubanne, P., and Cailletaud, G.. Single Crystal Modeling for Structural Calculations : Part 1—Model Presentation, Journal of Engineering Materials and Technology, 113(1): 162–170. 1991. [2] Chen, Z., Lenthe, W., Stinville, J.C. et al. High-Resolution Deformation Mapping Across Large Fields of View Using Scanning Electron Microscopy and Digital Image Correlation. Exp Mech 58, 1407–1421 (2018). https://doi.org/10.1007/s11340-018-0419-y [3] Reischig, P. and Ludwig, W. Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction, Current Opinion in Solid State and Materials Science, 24(5): 100851. 2020.

ABSTRACT. When the elastic properties of structured materials become direction-dependent, the number of descriptors of their elastic properties (e.g., the elasticity tensor moduli) increases. In two dimensions (2D), for example, an anisotropic material can be described by up to 6 independent elasticity tensor moduli, as opposed to 2, when the properties are direction-independent. Such a high number of independent elastic moduli expands the design space of structured materials, and leads to unusual phenomena, such as materials that can shear under uniaxial compression, or materials presenting shear-normal coupled deformations. These coupled deformations have applications ranging from shape-morphing to wave mode-conversion of longitudinal and shear waves. However, this increased design space makes it challenging to understand structure-property relations. There are no clear design rules, to understand how the architectural symmetries directly correlate to the observed structural properties and their moduli. There are also no well-defined upper and lower bounds on these moduli equivalent to the well-known Hashin-Shtrikman bounds on isotropic elasticity. This range is known as G-closure and provides limits for achievable tensors. In our work, we construct a database of two-phase periodic anisotropic unit-cell geometries, using a method inspired by the modeling of phase separation in spinodal decomposition. We utilize the database to visualize regions in the high dimensional design and property space and identify extremal properties that are yet to be explored. The constructed database is compared against properties achieved by hierarchical laminates, which are known to cover a vast design space. We further validate the elastic moduli of representative geometries from the database using mechanical testing on additively manufactured samples. We discuss the role of invariants of the elasticity tensors and how they can be related to the bounds on anisotropic elastic moduli.

ABSTRACT. We present a method for the numerical computation of representative volume element (RVE) in the context of high-order electromechanical theory, which relies on the construction of a generalized-periodic Cartesian B-Spline approximation space [1]. The geometry is unfitted to the mesh, and described by a periodic level set function. The imposition of generic macroscopic fields (strains/stresses and electric fields/electric displacements) is naturally allowed as strong Dirichlet/Neumann macroscopic conditions.

We apply the proposed method to study non-piezoelectric architected metamaterials with ap parent piezoelectric behavior thanks to the flexoelectric effect (coupling between polarization and strain gradient). In particular, we perform multi-objective topology optimization of flexoelectric metamaterial RVEs by means of genetic algorithms [2]. We find the Pareto fronts where area fraction is minimized and different apparent piezoelectric coefficients (stress/strain sensor/actuator) are maximized.

Overall, we find RVE topologies exhibiting a competitive apparent piezoelectric behavior as compared to reference piezoelectric materials such as quartz and PZT ceramics.

References [1] J. Barceló-Mercader, D. Codony, A. Mocci, and I. Arias, “Computational homogenization of higher-order electro-mechanical materials with built-in generalized periodicity conditions”, arXiv preprint arXiv:2311.08196, 2023. [2] F. Greco, D. Codony, H. Mohammadi, S. Fernández-Méndez, and I. Arias, “Topology optimization of flexoelectric metamaterials with apparent piezoelectricity,” Journal of the Mechanics and Physics of Solids, vol. 183, p. 105477, 10 2023.

ABSTRACT. Architecting heterogeneous materials on various (single) crystal lattices has been in a focal point of research with the recent progress in three-dimensional printing and additive manufacturing technologies across a wide range of length scales. In this work, we combine experiments and numerical simulations to design polycrystalline architected materials that exhibit superb elastic and inelastic features under extreme deformation conditions, inspired by polycrystalline metallic materials comprising single crystalline grains and their boundaries. First, we present a simple yet systematic design principle for the polycrystalline microstructures with varying grain sizes. We then fabricated the polycrystalline microstructures using a high-resolution, multi-material 3D printer and conducted large strain mechanical tests on the 3D-printed prototypes under plane-strain cyclic loading scenarios. Our experimental and numerical results revealed that elastic stiffness and plastic strength can be dramatically enhanced as the grain size decreases in these 3D-printed polycrystalline microstructures; furthermore, the connectivity (or strength) throughout the grain boundary network was found to play a crucial role in determining the grain size-dependent stiffness and strength, and their anisotropies. In addition to the grain size-dependent mechanical features, we examined catastrophic failure and “reusability” in the 3D-printed polycrystalline microstructures under large strain cyclic loading conditions, where we observed that cracks mainly initiate in the vicinity of two adjacent grains with a significant difference in their lattice orientations. Moreover, the high-angle grain boundaries were found to efficiently stop the crack propagation and mitigate the catastrophic failure throughout the polycrystalline network. Altogether, our work demonstrates a simple yet physically intuitive microstructure-topology-based approach for designing the polycrystalline architected materials that exhibit outstanding combinations of elastic and inelastic features involving stiffness, strength, energy dissipation, and reusability under harsh mechanical environments.

ABSTRACT. This study employs the Essential Work of Fracture (EWF) concept to evaluate the interfacial fracture toughness of bioinspired interfaces between soft-hard polymer phases. The experimental framework utilizes a model material system with Polylactic Acid (PLA) as the hard phase and Thermoplastic Polyurethane (TPU) as the soft phase. Employing the Fused Filament Fabrication (FFF) technique, bioinspired sutural interfaces are created, characterized by interpenetrating soft and hard protrusions. The modulation of a critical parameter in the FFF process enables the variation of interpenetration length of protrusions, thereby achieving a spectrum of interfacial strength and toughness. The determination of essential work of fracture from double edge notch tension samples, with varied ligament sizes, allows for the specific EWF measurement. This specific EWF is found to align with the initiation value of plane strain interfacial fracture toughness obtained through the double cantilever beam test. Therefore, the proposed approach asserts the elimination of the need for complex interfacial fracture tests, such as the double cantilever beam test. A noteworthy discovery is the establishment of a correlation between specific plastic energy dissipation and protrusion length. This correlation suggests an increased plastic dissipation with longer protrusions within the investigated bioinspired interface. Due to this heightened plastic energy dissipation, the shape of the interfacial nominal stress-displacement curves demonstrates substantial dependence on interface morphology, shifting from a triangular shape to a trapezoidal shape as protrusion length increases. These findings offer valuable insights into the mechanics of bioinspired interfaces, presenting a more efficient and nuanced approach to characterizing their fracture properties.

ABSTRACT. Magnetoactive elastomers (MAEs) are composite materials whose mechanical behavior can be tuned by an external magnetic field. This characteristic leads to numerous applications such as soft robots, sensors, and noise barriers. This work aims to provide a guideline to actively and remotely control microstructure transformations and mechanical properties in magnetoactive soft composites by triggering magnetic-induced instabilities. For this purpose, a framework to perform instability analysis of MAEs is proposed. Specifically, take the laminates as an example, numerical and analytical models of layered MAEs with soft/hard magnetic inclusions are developed based on the finite element method and classical magneto-elasticity theory. Buckling and post-buckling analysis are performed to predict the onsets of instabilities at the microscopic and macroscopic length scales. Based on the established models, we obtained the relationships between critical stretch (critical wavelength) and magnetic field level. Further, we have studied the effect of volume fraction, additional invariants, and initial susceptibility on the onset of magneto-mechanical instabilities.

ABSTRACT. This work investigates macroscopic magneto-mechanical instabilities formed at the surface of stiff magnetorheological elastomer (MRE) films bonded to a soft passive substrate undergoing finite strains and large magnetic fields, using full-field 3D numerical simulations. We exploit a recently proposed microstructure-guided explicit analytical model based on a simple F-B variational energy formulation with few calibration parameters. This allows for an effective numerical implementation of the model to solve macroscopic boundary value problems for a wide range of parameters, such as the magnetic particle volume fraction and the material properties of the individual constituents. The model can thus be used to study numerically the dependence of instabilities on both the magnetic and mechanical properties of film/substrate system in a three-dimensional finite element setting. We first discuss some of the numerical limitations and assumptions used in this work, and then establish a 3D boundary value domain based on mesh sensitivity analysis. A parametric study is also performed to analyze the influence of different material parameters on the arising 3D patterns. Finally, we investigate both experimentally and numerically the instability patterns formed in a heterogeneous MRE layer comprising four magnetoactive discs embedded in a soft silicone square substrate as a function of the applied magnetic field.

ABSTRACT. Defect tolerance trough high work-hardening in parts produced by additive manufacturing has been recently proven efficient in beta metastable Ti alloys. However, this alloy family does not meet the necessary yield strength levels of the aerospace industry. In the present study, alpha+alpha' microstructures are shown to exhibit never reached strength/work hardening balances. First, the proof of concept is evidenced in the well-known Ti-Al6-V4 alloy. It is shown that increased work-hardening is obtained by a novel deformation mechanism in the martensite of such dual-phase structures: Reorientation Induced Plasticity or RIP effect. Based on these findings, new alloy design rules are then proposed to increase the work-hardening behavior of lean alpha+beta alloys. They are shown to be particularly efficient on 3 different alloys. Reorientation Induced Plasticity is responsible for this unique behaviour. A large work-hardening level can be obtained while preserving high yield strength levels provided the compositions and annealing conditions are properly optimized.

ABSTRACT. In recent years, additive manufacturing of Ti-6Al-4V (Ti64) alloy by Laser Powder Bed Fusion (L-PBF) became mature enough to consider manufacturing structural components for specific applications. Nevertheless, post-processing operations seem to be unavoidable to meet the product requirements in term of static and dynamic mechanical behavior.

As a consequence of high cooling rates involved during L-PBF, as-printed Ti64 parts present an α’ martensitic microstructure consisting of fine, hierarchical and entangled needles. The α’ phase grows upon cooling in columnar parent β grains whose morphological and crystallographic texture is oriented parallel to the building direction. This microstructural anisotropy affects the tensile properties and in particular the ductility of the samples built with different orientation.

In order to relieve the residual stresses formed during the process and to decompose the martensitic phase into an equilibrium α+β mixture, post-processing heat treatments (HT) are performed on Ti64 as-built parts in the sub-transus range. The induced phase transformation helps to balance the strength / ductility compromise that mainly depends on α laths width and β phase fraction.

In this study, 5 post-processing HT ranging from 720°C to 980°C were performed on Ti64 bars, built with vertical and horizontal orientations, that are then machined into tensile specimens. The microstructure and tensile properties in the as-built condition and after HT are presented extensively. In particular, the embrittlement mechanisms that possibly affect the elongation anisotropy are investigated through interrupted tensile tests coupled with EBSD characterization. Finally, one discusses the effect of HT on the mechanical anisotropy evolution.

ABSTRACT. Currently most of the titanium scraps are collected, sent out of Europe and re-melted into ingots for further use. In the present study, we have demonstrated that it is possible to valorize titanium Ti-6Al-4V scrap into high added value powders for various manufacturing technologies (SLM and DED). The different steps needed to get the final product (cleaning, hydrogenation-dehydrogenation (HDH) process, grinding and sieving) will be described. The obtained powder has been characterized. Both physical (morphology, particle size, chemistry) and processability (flowability, compaction) characteristics have been determined and compared to commercial titanium TA6V powder. Then, some preliminaries trials of additive manufacturing have been performed with laser powder bed fusion (SLM) and laser metal deposition (DED) technics. Material health and mechanical properties have been assessed and also compared to commercial titanium TA6V powder. Regarding the recycling of the titanium chips, a lot of issues have been tackled to successfully manage to produce the right titanium powder.

ABSTRACT. Additive manufacturing (AM) processes allow for the personalisation of orthopaedic implants. However, permanent implants are not always suitable, since the implant is no more needed once the fracture is repaired. As such, degradable implants, among which Iron (Fe), Zinc (Zn) or Magnesium (Mg) are being studied, would allow a temporary repair function and will degrade after few months. But AM of such alloys, especially Mg, is extremely challenging. Beside laser powder bed fusion (L-PBF), the sinter-based AM techniques are promising to tailor porosity at various scales, leading to customised properties. However, the sintering process of magnesium is the main challenge to overcome as magnesium is one of the most reactive metal for oxidation issue. In this presentation, we will present a sinter-based AM technique to 3D print Mg parts, called robocasting or direct-ink writing. This 3D printing process consists of (i) extruding a paste filled with metallic particles (ii) debinding the organic components of the paste and (iii) pressureless sintering the final structures. The presentation will focus on optimising the debinding and sintering of the parts. We propose to study the liquid phase sintering of MgZnZr (ZK30) alloy. Due to the high reactivity of Mg, a thin oxide layer of approximately 7 nm forms at the surface of the particles. This thin layer acts as a diffusion barrier, thus to perform sintering this barrier must be overcome. Compared to pure Mg, the use of an alloy aims at tailoring the liquid phase proportion to sinter the parts. Using thermodynamic calculations and various in situ experiments such as differential scanning calorimetry (DSC), we optimized the sintering conditions in order to retain the complex shape of the printed material. The sintering set-up is described (atmosphere, temperature, type of confining materials). We managed to sinter, in a reproducible way, various 3D printed parts. Post mortem analyses were carried out, from micro-tomography to microstructural characterization, to link the sintering conditions to the properties of the sintered parts.

ABSTRACT. For decades, numerous efforts have been made to design structures against buckling and instabilities, which often lead to their catastrophic failure. By contrast, recent studies have shown that harnessing mechanical instabilities can provide structures with new features as negative stiffness and energy dissipation [1]. Domes are shell structures that can exhibit up to two stable states, mostly depending on geometric and material parameters [2]. Apart from its basis state, a dome can be subjected to snap-through buckling and remain stable in this state indefinitely over time in absence of external loadings, being then considered as bistable. Recently, studies showed that bistability of domes may be used for shape morphing of soft sheets [3] and mechanical programmability [4]. However, to design such structures based on multiple bistable units, the knowledge of the mechanical behavior of individual dome shells is required. Furthermore, the strain energy required to switch between both stability states (often referred to as the energy barrier) varies upon loading (i.e. snap-through instability) and unloading (i.e. snap-back instability), and is needed to determine an actuation strategy.

The present work exploits non-linear FEA and experimental measurements to explore the mechanical behavior of elastomeric dome shells. The mechanisms behind dome shell asymmetrical energy barrier are investigated. Single element snapping and bistability are computationally analyzed and results are compared with experiments. The strain energy required to switch between stable states is computed, and an asymmetry index is proposed. These results are expected to be used as a guideline to design morphing structures based on bistable dome shells.

[1] Zhang et al., Scientific Reports, 2019. [2] Brodland et al., International Journal of Solids and Structures, 1987. [3] Faber et al., Advanced Science, 2020. [4] Udani et al., Extreme Mechanics Letters, 2021.

ABSTRACT. Multistability in shell structures is common both in nature and - sometimes unintentionally - in manmade structures. It can be induced in diverse geometries by material anisotropy, residual stresses, surface texturing and creasing. Modelling of such structures is challenging due to the need to account for both bending and stretching energy when exploring the available stable geometries and the transition between states. Here, we focus on minimal surfaces and their isometric transformations thus allowing us to focus our mathematical treatment on the bending energy variation. At the same time, we employ anisotropy to tune multistability for this category of geometries. We confirm our results through physical demonstrators.

ABSTRACT. Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates—what is a petty frustration when placing a sticky band aid onto a knee is a more serious matter in the coating and painting industries. The geometry of curved surfaces and the mechanics of thin materials make this, apparently simple, procedure difficult: adhering two materials of different Gaussian curvature requires incompatible deformations. Nevertheless, sufficiently small sheets smoothly adhere to, for example, a sphere. We study in detail the threshold size below which smooth adhesion is possible and show that for very thin materials its failure occurs significantly sooner than expected from previous theoretical work. This earlier onset is the signature of buckling-induced delamination and not the dewetting-like transition previously assumed. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination accounting for the two buckling motifs that underlie partial delamination: shallow “rucks” and localized “folds”. We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experiments.

ABSTRACT. Achieving the transformation from a two-dimensional surface to a three-dimensional structure requires locally changing the curvature of the flat surface and therefore locally changing the metric of the surface, according to Egregium theorem. To build this type of flat structure, we manufacture channels within a silicone plate, using the direct ink writing (DIW) technique. This technique allows us to build channels of various diameters and different heights of the cross-section. By pressurizing the channels the plate deforms locally in the direction perpendicular to them.

We have found that by printing channels centered on the neutral plane of the plate, they allow us to change the metric depending on the applied pressure, and on the other hand, if the channels are outside the neutral plane, they allow us to change the local curvature. The flexibility of this manufacturing technique allows us to build plates with multiple channels in the same section, therefore we can locally change the curvature and metric depending on the pressures applied to the different channels.

Additionally, we explore the interaction of different sets of channels that are pressurized independently, exhibiting, in the same structure, different shapes and mechanical behaviors for different combinations of applied pressures. Finding that when the control of local curvature dominates the structures are stable and when the control of the metric dominates the structures can be multi-stable.

ABSTRACT. X-ray computed tomography (XCT) is a reliable tool for measuring internal flaws and microstructural features in engineering materials. As an extension to XCT, Digital Volume Correlation (DVC) methodology enables tracking 3D deformation field based on local grayscale contrast. Nevertheless, its applicability and spatial resolution have been limited by the need for tracer particles or inherent microstructural features that are distributed in the material volume. To address these limitations, we developed a Flux Enhanced Tomography for Correlation (FETC) technique that leverages inherent inhomogeneities in engineering materials (polymers to metals) to measure all nine components of the deformation gradient without relying on artificial X-ray tracers. Via this unprecedented full-filed measurement technique, the mechanical behaviour of various engineering polymers was examined, and new observations was made on the well-established rubber elasticity. It was found that many polymers undergo significant local volume changes but the overall volume remains constant during mechanical loading. The presence of a mobile phase within the material volume has been proved which gives rise to negative local bulk moduli. By extending its application on other materials, FETC is expected to bring more electrifying discoveries of new material physics.

ABSTRACT. A wide range of commonly used metals and alloys are susceptible to hydrogen embrittlement (HE), which currently limits the design of structures in many industrial sectors, notably energy and transportation. HE is strongly related to hydrogen interactions with the metal lattice structure and its crystallographic defects, such as interfaces, dislocations, second-phase particles and vacancies, as well as local mechanical states (hydrostatic stress and/or plastic strain). Therefore, understanding the underlying mechanisms of hydrogen-assisted fracture requires fit-for-purpose testing methodologies capable of capturing the specificities of the fracture mechanisms of each alloy-hydrogen system. This work shows recent developments in fracture testing for hydrogen-assisted intergranular cracking in nickel and hydrogen-assisted fracture of pipeline steels. The results provide new insights into the threshold conditions that determine the HE fracture mode and the preferred cracking path as a function of hydrogen concentration, depending on the hydrogen-containing environment to which the alloys are exposed to.

ABSTRACT. The detrimental effect of hydrogen on metals which manifests itself as a transition from a ductile to a brittle failure mode is simulated via a unified continuum-scale predictive framework. The so-called complete Gurson model, originally formulated for predicting ductile failure via voiding, is now enhanced to include failure due to decohesion. Hydrogen enhanced localized plasticity (HELP) is represented by the accelerated voiding process, while hydrogen enhanced decohesion (HEDE) manifests through a reduction in the decohesion threshold. This ductile-to-brittle transition, driven by local hydrogen concentration, is effectively captured by the model. It enables predictions of realistic embrittlement levels and the suppression of dimples on hydrogen-induced fracture surfaces. Being generic, versatile, and easy to implement, the model may serve as a basis for interpretation of laboratory experiments and enable the transferability of the laboratory results to engineering structural assessment in hydrogen environment. Additionally, this talk introduces recent advances in incorporating the hydrogen enhanced strain induced vacancy (HESIV) mechanism into this modeling framework.

ABSTRACT. In this work, the effect of hydrogen on the dislocation-based plastic behavior of α-Fe was examined by carrying out a multi-scale study. The influence of hydrogen concentration on the critical shear stress required for screw dislocation glide was quantified at the atomic length scale. The obtained variation in dislocation glide behavior was utilized to develop an accurate continuum description to examine the dislocation-based plasticity in polycrystalline α-Fe. To enable this study, a new Fe-H interatomic potential was developed that provides an accurate description of various hydrogen - defect configurations, which is essential to accurately study the effect of hydrogen on dislocation glide behavior. The screw dislocation core reconstruction observed due to the presence hydrogen was validated by performing large-scale DFT calculations based on the DFT-FE framework. To comprehensively quantify the effect of varying hydrogen concentration on the dislocation glide mechanics, several atomistic simulations were carried out. Lastly, crystal plasticity simulations were performed to assess the ramifications of the atomistically observed variation in dislocation glide behavior introduced by hydrogen on the meso-scale deformation behavior of polycrystalline α-Fe.

ABSTRACT. The laboratory specimens used to assess the interlaminar fracture toughness of layered materials can be classified as either standardised or non-standardised. We term standardised a specimen extracted from, for example, a unidirectional composite laminate or an identical-adherend adhesive joint, such as metal-to-metal or composite-to-composite. Assessing fracture toughness using standardised specimens is a common practice guided by international test standards. We term non-standardised a specimen resulting from, for instance, unsymmetric or unbalanced laminates with an elastically coupled behaviour or residual thermal stresses (if cured at elevated temperature), bimaterial or multimaterial joints, or fibre metal laminates. There are certain issues in determining the interlaminar fracture toughness of such non-standardised specimens that inherently feature material or layup asymmetry with respect to the delamination plane. The double cantilever beam test and other well-known delamination tests are used to characterise the interlaminar fracture of these specimens. Nevertheless, a specimen with material or layup asymmetry will experience mixed-mode fracture at its crack front, even if it is remotely loaded in pure mode. Several fracture mode partitioning approaches have been proposed to extract the pure-mode fracture toughnesses, which will be discussed in this presentation. Next, we will elaborate on the critical effects of bending‒extension coupling and residual thermal stresses often appearing in non-standardised specimens by reviewing major data-reduction models that consider those effects. In laminated composites, in particular, the ply orientation angle difference at the delamination interface is another issue that critically affects the interlaminar fracture behaviour. For example, delaminations can migrate when this difference exceeds 15°. Experiments that study the effect of ply orientation at the delamination interface are hence impossible beyond that critical angle. The effects of an elastically coupled behaviour and residual thermal stresses may also appear in these laminated composites, further complicating the fracture toughness analysis.

ABSTRACT. Additively manufactured fiber-reinforced components (FRC) rapidly gain traction in the European aerospace and transport industry. This is attributed to their well-established benefits, including reduced machine, material, and labor costs, minimized manufacturing waste, and the utilization of more efficient materials. Despite these advantages, a notable drawback of additively manufactured components lies in their intricate and often tessellated geometry. This complexity gives rise to combined damage mechanisms, such as fiber pull-outs and matrix cracking, deviating from the conventional paradigm of "high strength and ductile metal". To address this challenge, the phase-field method emerges as a robust approach for damage modeling, offering capabilities to accurately resolve the initiation, propagation, branching, and merging of complex curvilinear crack topologies.

In this work, we revisit the cohesive phase-field model introduced in [Geelen, 2019] for isotropic domains and extend it to resolve intra-laminar damage response in 3D printed FRCs. The damage model incorporates a linear crack-surface density functional, exhibiting pure-elastic behavior until damage onset, and a quasi-quadratic degradation function which can be used to calibrate experimental strain softening curves, thereby accurately predicting quasi-brittle damage response in FRC.

The resulting coupled governing equations are discretized using the Virtual Element Method (VEM). It has been shown that the use of polygonal virtual elements achieves higher order FEM convergence [Aldakheel, 2018] in reduced computational costs. Furthermore, with its ability to handle irregular and complex geometries, the VEM addresses the challenges posed by the intricate and tessellated structures inherent in additively manufactured components. This integration holds the potential to optimize the discretization process, overcoming limitations associated with finer mesh requirements and mitigating the computational costs associated with conventional methods. The effectiveness and robustness of the combined methodology is explored within the context of 2D deformable domains and comparison is conducted between numerical models employing either quadrilateral/triangular meshes or polygonal meshes.

The research work was supported by the funding received in the framework of H.F.R.I call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union –NextGenerationEU (H.F.R.I. Project Number: 15097).

ABSTRACT. Recent advances in experimental techniques have made it possible to characterize the bulk microstructure and map cracks inside millimeter-sized samples. Meanwhile, mathematical and numerical tools, have been developed and applied to model the nucleation and growth of cracks in brittle materials. The phase-field method, originally formulated to model complex crack on a macroscopic scale, has recently been extended to gain more and more physical insight. Recent developments include extensions to account for an anisotropic fracture energy landscape, coupling with plasticity [1], or diffusion of chemical species. In this context, we focus our scope at the microstructure scale, on materials where brittle fracture is initiated and governed by local plastic activity, e.g. silicon-iron, tungsten or steels at low temperatures. The seminal work of Hall [2] and Petch [3] has shown how grain size is related to size effects on the yield and fracture strength. The role of grain boundaries and grain size on the fracture toughness is less clear as the fracture toughness exhibits a non-monotonic evolution with grain size in the micrometer range [4]. We present advances in modeling the coupling between crystal plasticity and brittle fracture. We recall how local stress heterogeneities and singularites can arise from dislocation self-interactions and interactions with grain boundaries. Therefore, we develop a modelling framework designed to capture plasticity-induced brittle fracture that accounts for a material lengthscale. We outline the role of this lengthscale in capturing characteristic grain-size effects observed for brittle crack nucleation and propagation in polycrystals.

[1] Brach, S., Tanné, E., Bourdin, B., and Bhattacharya, K.. Computer Methods in Applied Mechanics and Engineering 353 (2019): 44-65. [2] Hall, E. O. Proceedings of the Physical Society. Section B 64.9 (1951): 747. [3] Petch, N. J. Progress in Metal Physics 5 (1954): 1-52. [4] Reiser, J., and Hartmaier, A.. Scientific reports 10.1 (2020): 2739.

ABSTRACT. Duplex stainless steels (DSS) are used in corrosive environments thanks to their mechanical and chemical properties. Their static and cyclic behavior are well known within the conventional process framework. Since few years, these dual-phase materials are used in additive manufacturing (AM). However, DSS elaborated by laser powder bed fusion (LPBF) are fully ferritic in the as-built state. Heat treatments (HTs) are therefore mandatory to obtain the dual-phase material. Several HTs are possible and giving rise to different microstructures (phases ratio, grain morphology, texture). The influence of these HTs on static behavior of AM DSS was studied by many authors. But the effect on high cycle fatigue (HCF) behavior still lacks some investigation. This work aims to understand the influence of the microstructure and its competition with LPBF process induced defects on the HCF behavior of additively manufactured DSS SAF2507. Firstly, four microstructures were selected : (i) the as-built state which is fully ferritic, (ii) the 50-50 austenite-ferrite ratio with fine grain microstructure reminding the LPBF thermal history, (iii) the 50-50 austenite-ferrite ratio with coarser grains, and (iv) the hot isostatic pressure (HIP) microstructure. Secondly, tensile and torsional HCF strength were determined for each microstructure. Then, the fatigue fracture mechanisms were investigated by fractographic analysis. Finally, these microstructures were explicitly modeled using Neper software. CPFE simulations were performed to determine the microstructure sensitivity of the HCF strength. The experimental results show that there is a microstructure-defects competition for tensile HCF since both fine grains microstructure with defect and defect free coarser grains microstructure (HIP) improved fatigue life to the same extent. In contrary, torsional HCF is less sensitive to defects and defect free crack initiations were observed for microstructure having process induced defects. The CPFE analysis illustrates a preponderant effect of LPBF induced defects compared to the microstructure.

ABSTRACT. Ni-based superalloys are widely used in gas turbines. Nevertheless, the influence of the microstructure on the fatigue crack initiation mechanisms is not fully understood yet. This investigation analyzes the relationship between slip transfer and fatigue crack initiation in two solution-hardened alloys (Inconel 600 and Hastelloy C276) tested under fully-reversed cyclic deformation under strain control in the low-cycle fatigue regime. EBSD-based slip trace analysis was utilized to identify the active slip systems across after interrupted fatigue tests. Furthermore, the strain fields in the microstructure and the slip activity were captured by means of high-resolution digital image correlation after interrupted fatigue tests. This information was employed to analyze slip transfer and crack initiation at regular grain and twin boundaries. It was found that fatigue cracks were nucleated at grain and twin boundaries when the slip transfer across was blocked. This behavior was associated with stress concentrations at grain and twin boundaries as well as triple junctions that are enhanced under strain-controlled deformation while fatigue crack nucleation along slip bands parallel to twin boundaries was observed in other investigations carried out under stress-controlled loading.

ABSTRACT. The use of fatigue-resistant steel grades is critical in advancing the durability and reliability of railway components. Ferrite-pearlite steels are frequently employed due to their balance of strength and toughness. The existence of multiple grains with distinct orientations and sizes within such a polycrystalline material can result in non-uniform strain distributions, commonly referred to as strain heterogeneities. These heterogeneities have the potential to induce premature failure and limit material performance. Furthermore, the incorporation of heat treatments during the manufacturing process and plastic deformation during operation generates micro-structural gradients, modifying the material's mechanical properties. Nevertheless, the effect of these microstructure gradients on fatigue characteristics remains ambiguous.

In response, we devised an experimental approach incorporating in-situ optical-based Digital Image Correlation (DIC) to quantify local strain during Low Cycle Fatigue (LCF) loading. Flat specimens were extracted at various depths from a railway wheel composed of ER7 steel, with a microstructure featuring ferrite and pearlite. These specimens were designed with a semi-circular notch. A Region of Interest (ROI) was marked, and a speckle pattern was applied to the surface. LCF tests were performed, wherein images were captured of the speckle pattern at cyclic load peaks. Subsequently, the DIC technique was employed to compute displacement fields. These fields were spatially correlated onto the surface microstructure and Electron Back-scatter Diffraction (EBSD) data of the ROI, captured before the test. This methodology allowed for the identification of strain localization and potential sites for the initiation of cracks.

A prior study in monotonic tension on ER7 steel reveals varied deformation behaviours, such as early plasticity and stress plateau, influenced by microstructural differences. Statistical analysis identified correlations between pro-eutectoid ferrite grains prone to deformation and adjacent pearlite nodules. Our study aims to understand the early strain localization patterns in ferrite-pearlite steel with a microstructure gradient under cyclic loading.

ABSTRACT. In aeronautical industry, blade/disk root attachments are subjected to fretting-fatigue conditions that can lead to cracking damage and reduce significantly the service fatigue life. To characterize the crack initiation risk in fretting-fatigue, a non-local approach was proposed. The approach consists of partitioning in a reference frame attached to the contact front, the velocity field as the product between non-local variables and spatial shape functions. Based on non-local variables, non-local fretting-fatigue crack initiation criteria are formulated. Thanks to the non-intrusive nature of the partitioning technique, the non-local approach can be applied to any displacement field derived from an independent calculation. In this paper, the approach is applied to a displacement field computed by Digital Image Correlation technique from images captured during fretting-fatigue experiment under variable normal loading condition. The time variability of the normal load implies a variability in time and space of the contact front position, leading to a spatial dispersion of contact damage. One of the main challenge in this study is the detection of contact front position for each time increment. An incorrect choice of contact front position leads to an incorrect identification of non-local variables. A physics-based methodology for the detection of contact front position was therefore developed to track the contact front position during image analysis. The validity of the methodology was first tested and proven on displacement fields obtained by numerical simulation for configurations where the position of the contact front is known analytically. By adding random noise to the displacement fields derived from numerical simulation, the contact front search algorithm detect the same positions as when there is no noise, demonstrating the robustness of the methodology. With this methodology, the evolution of contact front position is tracked during image analysis and for each position, the non-local variables are extracted.

ABSTRACT. Energy transduction, i.e. the ability to transform mechanical energy into electrical energy and vice-versa is the core of current technologies for sensors, actuators and energy harvesters which are extensively used in a wide range of applications, such as consumer electronics, car sensors and diagnosis techniques to name a few. Most of these technologies rely on piezoelectricity, the coupling between polarization and strain. In recent decades, flexoelectricity, a universal electromechanical coupling, has received increasing attention as a promising alternative for electromechanical applications. Flexoelectricity is the two-way coupling between strain gradient and polarization, and conversely the coupling between polarization gradient and strain [1]. It is a gradient effect and thus scales inversely to size, becoming relevant only at sub-micron sizes in most materials. Nevertheless, developments in nanotechnologies have enabled a miniaturization of electromechanical devices reaching sizes where flexoelectricity becomes important [2]. Thus, a full understanding of the underlying physical mechanisms becomes essential towards developing engineering tools to optimize the performance of piezoelectric devices and to design new active metamaterials exploiting flexoelectricity [3, 4]. One aspect which remains elusive is the effect of surfaces on the overall flexoelectric response of finite samples [5]. Surface piezoelectricity has been claimed as one possible source of discrepancy between theoretical estimates and experimental measures of flexoelectric coefficients [1]. In this work, we develop a model to account for surface effects in a mathematical and computational framework for flexoelectricity and explore avenues towards the differential characterization of both mechanisms.

References

[1] P. Zubko, G. Catalan, and A. K. Tagantsev, “Flexoelectric effect in solids,” Annual Review of Materials Research, vol. 25, pp. 946–974, 2013. [2] B. Wang, Y. Gu, S. Zhang, and L.-Q. Chen, “Flexoelectricity in solids: Progress, challenges, and perspectives,” Progress in Materials Science, vol. 106, p. 100570, 2019. [3] A. Mocci, J. Barceló-Mercader, D. Codony, and I. Arias, “Geometrically polarized architected dielectrics with apparent piezoelectricity,” Journal of the Mechanics and Physics of Solids, vol. 157, p. 104643, 2021. [4] F. Greco, D. Codony, H. Mohammadi, S. Fernández-Méndez, and I. Arias, “Topology optimization of flexoelectric metamaterials with apparent piezoelectricity,” Journal of the Mechanics and Physics of Solids, vol. 183, p. 105477, 10 2023. [5] A. S. Yurkov and A. K. Tagantsev, “Strong surface effect on direct bulk flexoelectric response in solids,” Applied Physics Letters, vol. 108, no. 2, p. 022904, 2016.

ABSTRACT. Particle-filled magnetorheological elastomers (MREs) represent a sophisticated class of two-phase composites, where metallic magnetic micron-sized particles are randomly dispersed within a non-magnetic and mechanically soft elastomer matrix. Recently, magnetoactive polymer foams have been produced, resulting in a lightweight three-phase porous material characterized by millimeter-sized voids. The magnetic and mechanical properties of the resulting active foam can be tuned to meet specific performance requirements. This can be done through the control of the manufacturing process parameters and by adjusting the quantity of magnetic particles. Motivated by these advancements, this study employs numerical simulations to investigate the response of MRE foams under finite deformations and in the presence of magnetic fields. In addition, we propose analytical models that capture the effective responses of these materials.

ABSTRACT. Micromagnetic simulations are computationally demanding and hence usually restricted to systems of strongly limited size. In practice, we typically either choose to investigate microscopic systems or we use phenomenological magnetic material models on the macroscale, which are often linearized around the working point. Continuum models on an intermediate scale (mesoscale) are mostly missing. On this scale, there are too many domains for economic micromagnetic simulations but the domain structure has a distinct effect on the overall system behavior. To address the problem, we devised a continuum theory for magnetic materials being dominated by stripe-shaped domains (the term 'stripe-shaped domains' is used to distinguish the considered domain structure from the established term 'stripe domains'). We derive a mesoscopic potential starting from a potential-based kinematical description of continuously distributed stripe-shaped domain walls. Our formulation of the mesoscopic theory is based on a few fields with physically meaningful microscopic interpretation. A phenomenological closure-domain extension completes the picture and allows us to introduce a constrained energy minimization principle. We propose a monolithic finite-element based numerical solution algorithm and, based on a consistent linearization of the numerical algorithm, we obtain quadratic convergence for the nonlinear solution procedure. A first simple examination of the theory is preformed by simulating a thin film with spatially and temporally non-constant effective anisotropy. We find the results to be consistent with analytical predictions.

ABSTRACT. Energy harvesters are an evolving technology for the Internet of Things as well as for all areas in which devices and sensors are operated with low power consumption. In general, they offer the possibility to harvest electrical energy from ambient energy sources. One way of harvesting is thereby to use the piezoelectric effect to convert ambient vibrations into electrical energy. To also utilize occurring thermal fluctuations, the pyroelectric effect can be used. Since both effects occur simultaneously in some materials, the combination of both effects offers the possibility of increasing the harvested energy. However, since the energy harvested is typically too low to continuously power devices, the base structure has to be attached to an electric circuit that fulfills the purpose of rectifying, accumulating and storing the electric signal of the base structure. The simulation of such a pyropiezoelectric energy harvesting structure together with its attached electric circuit is the main topic of the presentation. The base structure is modeled via linear thermopiezoelectricity and solved with the finite element method, taking into account the connected circuit by means of appropriate boundary conditions. All three fields (mechanical, electrical and thermal) are fully coupled and solved simultaneously so that all coupling phenomena can be considered. Since dynamic contributions for the mechanical and thermal field have to be taken into account, details on the time integration methods used to ensure convergence are given. To illustrate the practical applicability of the simulation approach, results for numerical examples are given and discussed.

ABSTRACT. The estimated prevalence of peripheral arterial disease (PAD) is over 240 million people globally. End-stage treatment involves a bypass conduit to restore blood flow to limbs affected by critical limb ischemia. While conduit choices include xenografts and synthetic grafts, the use of autografts remains the gold standard, with better long-term outcomes for patients. The great saphenous vein (GSV) is the predominant autograft utilised, but approximately 40% of patients do not have sufficient GSV available. This leads to the over-use of synthetic grafts and consequently poorer patient outcomes due to their lower patency rates and an increased need for surgical revision. Currently, varicose (VV), and peripheral veins such as the popliteal (PV), superficial femoral (SFV) and tibial (TV) veins are not used as autograft options, despite a paucity of evidence demonstrating their lack of suitability as a conduit option. As the structure of the microenvironment influences the mechanical response of the surrounding tissue a robust investigation into the micromechanical and microstructural integrity of VV and peripheral veins would allow clinicians to make a more informed decision on whether these veins are suitable conduits. Consequently, this study micromechanically (using a novel mircoindentation approach) and structurally (using histology) characterises VV and peripheral veins to, for the first time, scientifically evidence their suitability as a bypass conduit, using the GSV for comparison analysis. Mechanical data show no significance between the Eeff of GSV and VV. The collagen content for GSV and VV was approximately 19% and 20% respectively. The results demonstrates, both mechanically and structurally, that VV have the potential to be used as a conduit option for patients who require bypass surgeries, thereby allowing for increased autograft options and improved long-term patient outcomes.

ABSTRACT. Cells avoid cyclic strain, as they orient perpendicular to the direction of applied cyclic strain on the underlying 2D substrate. This alignment is usually attributed to stress-fiber reorganization. However, experimental observations suggest that cell morphology and cytoskeletal stress-fiber organization are interconnected during cellular reorientation under cyclic loading. In this work, we developed a statistical mechanics framework that incorporates the stress-fiber organization, and cell morphology as well as their coupled evolution. The framework predicts the probability distribution of cell area, aspect ratio, and orientation, which agree well with the correspodning statistics obtained from experiments. Moreover, the framework proposes that cell achieve their final orientations by rotating from their initial configurations, instead of undergoing cellular straining. Our framework uncovers physical insights into the coupled dynamics of cell morphology and stress-fibers, and proposes a new mechanism governing cellular organization in cyclically strained tissues.

ABSTRACT. Understanding twinning in textured Mg alloys and ascertaining its correlation with microstructure can promote the design of polycrystals with controlled twinning during deformation. Here, twin nucleation in textured Mg alloys was studied using electron back-scattered diffraction (EBSD) in samples deformed in tension along different orientations in more than 3000 grains. In addition, 28 relevant parameters, categorized into different groups (loading condition, grain shape, apparent Schmid factors (SF), and grain boundary features) were recorded for each grain. This dataset was used for training Bayesian Networks models to analyze the influence of microstructural features on the nucleation of extension twins in Mg alloys. It was found that twin nucleation is favored in larger grains and in grains with high twinning SFs, but also that twins may form in grains with very low or even negative twinning SFs if they have at least one smaller neighboring grain and another one (or the same) that is more rigid. Moreover, twinning of small grains with high twinning SFs is also favored if they have low basal slip SFs and have at least one neighboring grain with a high basal slip SF that will deform easily. Finally, via in-situ EBSD, it was confirmed that anomalous non-Schmid extension twins nucleate at the onset of plastic deformation mainly at or near triple point grain boundaries accompanied by the localized compressive stress and due to the severe strain incompatibility between neighbor grains, stemming from the different slip-induced lattice rotations. Moreover, these anomalous twins could grow with the applied strain due to the continuous activation of <a> basal slip in different grains, which enhanced the strain incompatibility. This reveals the role of many-body relationships, including differences in stiffness and size between a given grain and its neighbors, to assess extension twin nucleation and growth in grains unfavorably oriented for twinning.

ABSTRACT. Conventional metallurgy is based on thermomechanical processes. The coupling between strain and temperature during these processes leads to grain boundary migration, recovery and recrystallization mechanisms. Although these mechanisms have been observed and studied for a long time, they are yet to be fully understood. Therefore, it is of particular interest to have a numerical model that can predict the final microstructure of a given material under specific stress and temperature conditions. To achieve this, it is necessary to couple two models: one that predicts microstructure evolution caused by deformation and the other for that predicts evolution caused by temperature. This was accomplished using a coupled phase-field-Cosserat model. However, to quantitatively predict microstructure evolution, the model needs to be calibrated against experimental observations. This study focuses on the microstructural evolution of pure aluminium (99.999 %) during deformation, both at room and high temperatures. First, in situ SEM tensile tests coupled with EBSD analysis are conducted at room temperature to assess the modification of crystallographic orientation. The results, including strain and crystal lattice reorientation, are compared to those obtained from crystal plasticity finite element method (CPFEM) simulations. To obtain an accurate description of the initial microstructure, the sample is characterized using diffraction contrast tomography. This provides a 3D orientation map, which is used to construct the synthetic microstructure. The comparison between the numerical and experimental microstructural evolutions enables fine calibration of the CPFEM simulations and verification of the model’s ability to accurately reproduce lattice reorientation and energy accumulation resulting from plastic deformation. The calibration procedure will then be carried out similarly using hot temperature SEM tensile tests coupled with EBSD analysis. This will allow us to proceed with the calibration of our coupled phase-field-Cosserat model for predicting dynamic recrystallization in polycrystalline metals.

ABSTRACT. In the present study, uniaxial low cycle fatigue (LCF) tests were conducted on cold rolled 22MnB5 steel at two different strain amplitudes of 0.4% and 0.6%. Specimen tested at 0.4% strain amplitude shows initial cyclic softening followed by hardening, whereas 0.6% strain amplitude specimen shows initial hardening in continuation with softening and then secondary hardening. Interrupted tests were done when the material showed change in hardening behaviour. At the interrupted points, a detailed microstructure and bulk texture evolution was investigated using the electron backscattered diffraction (EBSD) and x-ray diffraction (XRD) techniques. From the microstructure evolution it is evident that the grain average misorientation (GAM) is more in the 0.6% strain amplitude compared to 0.4%. From 2-theta measurement the evolution of dislocation density was determined which aligned with the softening and hardening behaviour. i.e increases with the hardening and decreases with the softening. From the quantification of the texture components, it was observed that the fraction of the cube (100)<001> and the copper (112)<111> texture orientation is increased with the increase in the number of cycles for both the strain amplitudes.

ABSTRACT. Despite their widespread use, the ferroelectric switching mechanisms within lead zirconium titanate (PZT) ceramics are not well understood due to the complexities in characterizing a polycrystalline microstructure containing intragranular nanodomains and defects such as pores and precipitates. The grain orientation, misorientation to neighboring grains, proximity to defects, and initial domain structure can all influence the domain evolution during the application of an electric field. Furthermore, the domain evolution is influenced by couped thermo-electro-mechanical loading conditions. Here, we investigate the influences of the loading conditions and the initial microstructure on the domain evolution and resultant bulk ferroelectric response in PZT ceramics. We have developed an in-house electrical testing setup capable of capturing the time-resolved ferroelectric strain and bulk polarization as a function of the applied electric field. To connect the bulk ferroelectric response to the microstructural evolution, we use electron microscopy to characterize the microstructure before and after applying the electric field. Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) analysis are powerful tools to resolve nanodomain structures in polycrystalline ferroelectrics but have been underutilized due to a few technical challenges—including the possibility of locally switching domains and difficulties in identifying the unit cell inversion of 180-degree domains. We demonstrate techniques to overcome both challenges and obtain high resolution microstructural information about the grain orientations, domain structure, and defect distributions from EBSD scans and SEM images optimized for high domain contrast. These techniques are extended to the third dimension through FIB-SEM tomography, providing full three-dimensional microstructural data. The wealth of microstructural data obtained before and after different electrical load histories provides insight into the condition-specific ferroelectric switching mechanisms, which will guide materials-based design strategies at the microstructural level for better control of the bulk ferroelectric response.

ABSTRACT. In the context of Euro fusion structural integrity assessment of the fusion materials, the mode I fracture toughness of nanostructured freestanding tungsten thin films is investigated using the ultra-miniaturized crack-on-chip (COC) method. A MEMS-based process has followed to create on-chip test structures involving an actuator undergoing large tensile stresses and a notched specimen beam. Upon release from the substrate, the actuator applies a pulling force to the specimen. A crack initiates, propagates and arrests. Tungsten films with a 370 nm thickness were deposited using the DC magnetron sputtering under different deposition conditions. The films were characterised using grazing Incidence X-ray diffraction (GIXRD), surface curvature measurements, scanning electron microscope (SEM), and nano-indentation. The microstructure evolution, phase development, residual stress, and mechanical properties were explored to confirm the BCC α-phase similar to the bulk tungsten. Subsequent annealing was also applied to reduce the internal stresses of the selected W films in order to enhance the mechanical stability with respect to the cracking test method. The fracture toughness of the W thin films was assessed on-chip using a combination of scanning electron microscope (SEM) observations to measure the arrest crack length and finite element modelling (FEM) to extract the critical stress intensity factor KIc. The analysis was conducted on 90 successful test structures, resulting in an average fracture toughness value of 3.03 ± 0.64 MPa √m. This value is about 50 % of the fracture toughness of bulk tungsten recorded at room temperature, despite the film having a submicron thickness. This indicates the potential of this approach to provide valuable information about the fracture toughness of tungsten under irradiation.

ABSTRACT. Protective coatings are required to endure severe mechanical stresses, with their durability directly affecting that of the underlying device or system. These layers must therefore exhibit high mechanical performance, ideally maximizing all the components of the well-known strength-ductility-toughness triptych. In this work, we employed a “nanolamination” strategy to design a coating system that meets this complex portfolio of properties. It consists of a multilayered stack alternating amorphous Al2O3 thin films as hard brittle constituents and crystalline Al thin films as softer “gluing” and/or “crack arrestor” constituents, with individual thicknesses below 100 nm. Thanks to an in-depth study combining micro- nanomechanical tests (nanoindentation, lab-on-chip, microscratch, push-to-pull), electron microscopy (SEM, TEM) and numerical simulations (FEM), an optimal nanolaminate system was identified. This optimization methodology will be presented through the eye of the nanoindentation investigations.

ABSTRACT. Grain boundaries (GBs) play a pivotal role in the design and performance of hard coatings. Our study focuses on understanding their impact on the fracture toughness of around 2 µm thick sputtered AlN, CrN/AlN multi-layered, and CrN hard coatings. For this purpose, we employed bridge notch cantilever bending tests on columnar grain boundary structures, aligning the notches both parallel and perpendicular to the coating’s growth direction. Our bridge geometry was optimized in such a way that the crack initiation occurs at the material bridges. Subsequently, the crack arrests and forms a natural sharp through thickness crack at which final fracture occurs. This way, not only three different fracture toughness values can be obtained from a single experiment, but also a very localized determination of the toughness value becomes possible with much reduced scatters in the data. We found that the GB orientation greatly influences the microscale fracture toughness. Notably, the deflection of cracks running perpendicular to the growth direction resulted in a significant increase of the fracture toughness, by around 10%. Furthermore, we observed that an epitaxial structure without GBs exhibits a higher fracture toughness compared to the columnar grain structure. The bridge with the epitaxial structure demonstrated a fracture toughness of 4.1±0.4 MPa·m1/2, which is higher compared to 3.0 ± 0.3 MPa·m1/2 of the bridge with the columnar grain structure. In the talk, the method of crack arrest upon bridge failure and its use for the determination of fracture toughness values in confined volumes will presented and discussed.

ABSTRACT. The computational bottleneck of reduced order models (ROMs) in nonlinear homogenization is usually given by the local material laws, which need to be evaluated in a large number of microscopic integration points. Hyper-reduction methods use only a small subset of the integration points and reach tremendous speed-ups at high accuracy. However, the underintegration breaks the overall compatibility of the microscopic strain field and is in this sense disrespecting the microscopic boundary value problem. Here, a new type of generalized integration points is introduced in strain space in order to remedy this shortcoming. Being inspired by results from nonlinear homogenization theory, the concept of statistical compatibility is developed and forms the theoretical basis for the new integration points, which respect the compatibility of the microscopic strain field in a statistical sense. The statistically compatible integration points can be derived offline and replace the conventional ones in a Galerkin-projection based setting with global modes identified via proper orthogonal decomposition (POD). The method is tested for various reinforced composites, indicating that 10-20 integration points are often sufficient to reach errors smaller than 3%, with CPU-times in the μs-range (per time step). A possible extension of the method for problems with higher nonlinearity and stronger field fluctuations is discussed within the context of a porous microstructure.

ABSTRACT. Thanks to its exceptional mechanical and physical properties, graphene has attracted researchers from various engineering fields. A thorough understanding of its mechanical behavior is essential to fully exploit its potential. However, due to the small scale of this material, only a limited number of experimental tests have been conducted. Therefore, the development of accurate mechanical models for graphene mechanics is crucial. In this study, a molecular mechanics model in nonlinear elasticity is introduced to investigate the size effect in graphene membranes. It is observed that the response of graphene remains unchanged beyond a certain threshold size. This threshold size marks the transition to the continuum theory, which is developed as a hyperelastic membrane model. Explicit relations between stretches and stresses of the membrane under large strains are derived for both uniaxial and equibiaxial loads. Unlike other continuum models in the literature, the approach proposed in this work is entirely developed in nonlinear elasticity, serving as a foundation for accurate predictions of graphene mechanics under stress states of practical interest.

ABSTRACT. Graphene-based architectures has attracted attention in diverse applications ranging from guiding wave and energy materials, to water desalination. Understanding the wave propagation in such materials is paramount for applications with exposure to dynamic loading. In this presentation, we address perfect architectures including single- as well as multi-layer graphene and (armchair and zigzag) carbon nanotube. Employing the wave finite element method and considering geometric nonlinearity, the corresponding unit cells are homogenized to study the wave propagation, dispersion relations and band structures. The generalized continuum theory of second-strain gradient elasticity will be used to capture the nonclassical features and comparatively look into the classical, first-strain and second-strain gradient elasticity theories.

Acknowledgements. This work is funded by the European Union’s Horizon Europe Programme (NANOWAVE) under the Marie Skłodowska-Curie Action grant agreement No. 101105373.

References: [1] Yang B., Mousavi M., 2024, Nonlinear dynamic behavior of carbon nanotubes incorporating size effects. International Journal of Mechanical Sciences. Accepted. [2] Yang B., Fantuzzi N., Bacciocchi M., Fabbrocino F., Mousavi M., 2024, Nonlinear wave propagation in graphene incorporating second strain gradient theory. Under review.

ABSTRACT. While ideal minimum-energy grain boundary structures are rarely encountered in actual polycrystalline aggregates, they are usually the only structures considered when characterizing grain boundaries. This limited perspective provides an incomplete view of the structural variability of grain boundaries which has been observed experimentally and which has been indicated by molecular dynamics simulations in several instances. In this study, the possibilities in using phase field crystal (PFC) modeling as a means for exploration of metastable grain boundary states is investigated. For this purpose, PFC is employed in a systematic search of grain boundary variants, based on gamma-surface sampling. Taking a range of symmetric tilt boundaries in FCC bicrystals as a demonstration case, it is shown that PFC indeed provides a useful tool for evaluating the structural multiplicity of grain boundaries. In addition, it is shown that a set of microscopic degrees of freedom (DOF) must be considered in addition to the grain boundaries five macroscopic DOF when identifying variants in structure. This set of microscopic DOF comprises three components of relative crystal translation, plus one DOF describing the atomic density in the grain boundary region. To further illustrate the implications of a multitude of structural variants being possible, grain boundary energy is taken as an example of a key thermodynamic property which is shown to exhibit a considerable spread with variations in the microscopic DOF, at constant macroscopic DOF. The findings underline the need to consider a spectrum of GB energies for each macroscopic GB configuration, rather than just a single value corresponding to an idealized minimum-energy structure, as is usually done. As part of the study, some computationally efficient strategies for setting up the PFC simulation model are also proposed.

ABSTRACT. The application of Phase Field Crystal (PFC) modeling has proven to be a versatile and effective numerical tool for analyzing crystalline microstructures. However, the predominant focus has been on bulk crystal behavior, with less exploration into crystal defects such as grain boundaries (GBs). This gap is particularly noticeable in crystal structures beyond face- and body-centered cubic crystals, such as diamond cubic (DC) crystal structures. For this reason, a systematic investigation of three different PFC models is performed to gauge the possibility of studying DC systems using PFC. The models employ combinations of two- and three-point correlations. One of the investigated models has been published previously and two are proposed modifications to established models. The findings indicate that the inclusion of a three-point correlation is crucial for stabilizing the expected DC GB structures, including the many multiplicities possible for each macroscopic degree of freedom. Despite inherent limitations in each model concerning the stabilized GB structures and phase stability performance, critical components within the PFC approach are identified as essential for successfully modeling DC structures.

ABSTRACT. During the heat treatment of alloys containing ordered precipitates, intergranular cracking can occur due to lattice misfits between the matrix and precipitates. The initiation and propagation of these cracks have been found to be linked to the location and growth of the precipitates. In order to enhance the understanding of intergranular cracking behavior, numerical models that are capable to accurately capture precipitation and growth over diffusive time scales need to be developed. The phase-field crystal (PFC) method presents a promising approach for modeling the behavior of ordered precipitates. This method allows for the creation of numerical models that can track the evolution of lattice structure on diffusive time scales, providing a comprehensive description of the behavior of ordered precipitates. In this contribution, different aspects of the implementation of a PFC model for disorderd to ordered phase transitions is presented. This includes a simple two point correlation function to stabilize a ordered square structure in two dimensions with predetermined elastic properties. The strain state is evaluated for the developed model for single- and multi-precipitate systems.

ABSTRACT. Twinning is a crucial process in many crystalline materials that undergo martensitic transformation, particularly in Shape Memory Alloys (SMAs) [1]. These unique materials can recover large strains under stress or thermal cycles due to the athermal nucleation and migration of twin interfaces [1]. While well-established theories [2] have successfully described twinning systems in SMAs, some twin systems are more commonly observed than others [3], and existing theories still need to understand this phenomenon completely. This knowledge gap limits the design of SMAs.

This study [4] focuses on the NiTi SMA, a prototypical example demonstrating the significant impact of twin interface mobility on twinning emergence. We provide an integrated approach by combining crystallographic theory, state-of-the-art atomistic modelling [5], topological model [6], and validation through high-resolution transmission electron micrographs [7]. Our atomistic simulations reveal a surprising trend where twinning is influenced by twinning stress rather than interfacial energy. These findings answer longstanding questions and illuminate the propagation mechanisms of twin interfaces beyond established theories of martensite crystallography. By discovering the critical role of interface mobility in twin formation, we can inform variant selection and guide the design of SMAs with enhanced functional performance.

[1] Otsuka, K. & Wayman, C. M. Shape memory materials (Cambridge University Press, 1999). [2] Ball, J. M. & James, R. D. Arch. for Ration. Mech. Analysis 100, 13–52, (1987). [3] Nishida, M., Ohgi, H., et al. Acta Metall. et Mater. 43, 1219–1227, (1995). [4] La Rosa, L. & Maresca, F. under review, (2023). [5] Ko, W.-S., Grabowski, B., et al. Phys. Rev. B 92, 134107, (2015). [6] Pond, R. C. & Hirth, J. P. Acta Mater. 151, 229–242, (2018). [7] Nishida, M., Yamauchi, K., et al. Acta Metall. et Mater. 43, 1229–1234, (1995).

ABSTRACT. Biodegradable polymers are materials designed to break down, and eventually disappear, after having fulfilled their structural function. They are widely used in healthcare applications such as sutures, stents, and tissue engineering scaffolds, where they eliminate the need for retrieval surgery. In this context, accurate predictions of the polymer service life and evolving mechanical properties is of fundamental importance. This study focuses on hydrolytic degradation, which involves the scission of polymer chains by reaction of susceptible backbone bones with water. We develop a reaction-diffusion continuum framework incorporating a discrete chain scission model able to describe various degradation mechanisms (random scission, chain-end scission, or any combination of these). Hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. This decoupling enables the identification of the chain scission mechanism from molecular weight reduction and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations of heterogeneous degradation, while retaining the predictive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. Generalisation of the continuum model to describe coupled degradation and mechanics will also be discussed, including the effect of degradation (decreasing molecular weight) on mechanical properties and the effect of stress on degradation rate.

ABSTRACT. Dysfunctions and anomalies in pelvic tissues cause numerous consultations and surgical interventions in women throughout their lives and during pregnancy. These issues are primarily attributed to the degradation or alteration of the biomechanical properties. For clinicians, understanding the mechanical behavior of this tissue is crucial for anticipating its degradation. This study aims to introduce an animal model using pig perineal tissues. To simplify the modelling process, the tissue is conceptualized as a multilayered tissue as it is mainly composed by three layers of skin, connective tissue, and anal sphincter muscles. The model relies on instrumented tensile tests, cyclic stress-relaxation, and unloading tests to effectively separate the influences of viscosity and damage effects on samples from the three layers as much as possible. Initial findings suggest a strong correlation between applied stretches, relaxation stress loss, and stress softening (Mullins effect), which is clearly observable during unloading sequences. A macroscopic modelling is employed to propose a 3D formulation including hyperviscoelasticity and stress softening. A set of parameters is identified to describe the mechanical behavior of the skin, connective tissue, and anal sphincter muscles during the loading, relaxation and unloading cyclic phases.

ABSTRACT. Fibrous networks are prevalent in both natural materials, ranging from body tissues to plants, and synthetic materials such as textiles, polymers and hydogels. Various properties of such materials, such as percolation and elastic moduli, can be studied by modelling them as stochastic networks. In stochastic networks, a given number of fibres are placed in a study domain and their intersection points are defined to act as cross links between the fibres. There is a large body of work dedicated to investigating the behaviour of random networks (a type of stochastic network where individual fibres are placed independently of each other), but local interaction of fibres, which results in departures from randomness, and are seen in materials such as polypeptide hydrogels, affect the structure of the network and are poorly studied and understood. In this talk, to investigate the effects of departures from randomness, we modify the process of generating the random network by allowing the probability of a fibre appearing and its orientation to depend on its proximity to existing fibres. Our results show that in more homogeneous networks, percolation occurs at a lower fibre density. Moreover, the rate of change of elastic moduli with respect to fibre density is lower for more homogeneous networks. In contrast, at densities much higher than the percolation threshold, various properties of these modified networks converge to those of unmodified stochastic fibre networks, which shows that the effects of departure from randomness are not considerable at high densities.

ABSTRACT. Ghost fishing refers to a gear’s capability to continue capturing marine life even after being lost. When an animal becomes entangled in a fishing net, the consequences are severe, including restricted movement, suffocation, injuries, and potential death due to starvation or predator attacks. To address this issue, biodegradable polymers such as poly(butylene succinate-co-adipate-co-terephthalate) (PBSAT) have been developed to reduce the mechanical impact of lost gear. While various studies have examined fishing nets made of biodegradable polymers, most have focused on gear selectivity, with limited attention given to the net structure’s mechanical properties and degradation. This study aims to characterize a PBSAT net as a multiscale structure, and to study its ageing in seawater using the same approach. Tensile tests on pristine samples showed that the PBSAT monofilament was more affected by the knotting than the commercial PA6 monofilament. X-ray tomography-derived curvature calculations demonstrated that breakage occurred mainly in high curvature zones for both materials. For ageing experiments, samples were immersed in natural seawater at different temperatures (15°C, 25°C, 40°C) for up to 8 months. Mechanical property degradation was observed across all temperatures and scales for PBSAT, while no changes were noted for PA6. High curvature zones induced high surface erosion after 240 days of immersion at 25°C. The alternative PBSAT nets tested in this study exhibited inadequate mechanical properties to replace conventional PA6 nets in commercial fisheries, primarily due to the material’s poor resistance within the knots. Moreover, the mechanical properties of the PBSAT net were highly sensitive to seawater ageing, showing accelerated degradation within the knots. The development of new biodegradable filaments will then need to be accompanied by testing and modelling.

ABSTRACT. Crumpled sheets and amorphous media exhibit memory effects and emergent computing capabilities but are difficult to control due to their highly disordered and uncontrolled geometry. Here we introduce an experimental platform that combines the geometric control of origami with the multistability of frustrated sheets, which allows to precisely and reproducibly couple and program multiple bistable hysteretic elements. We demonstrate that the geometry of the frustrated sheets controls the switching thresholds while the relative positions of the bistable elements set their interactions, giving rise to pathways (e.g., subharmonic orbits) inaccessible to systems of independent hysterons. Our work opens a new way for metamaterials with path-dependent responses and memory effects.

ABSTRACT. High-performance discontinuous composites manufactured with randomly oriented prepreg tapes have been developed to obtain an in-plane isotropic response combined with high stiffness and strength. Compared to composite laminates requiring a controlled lay-up, stochastic tow-based discontinuous composites also benefit from high manufacturability due to the random deposition of chopped tapes. Moreover, the use of thick, thin, and ultra-thin tapes has opened a design space with new structural applications. However, the high variability in terms of their 3D microstructures and mechanical properties imposes numerous challenges for numerical modelling. In particular, stochastic tow-based discontinuous composites show variations in tape waviness, tape draping, size of resin pockets, local fibre volume fractions, and thickness, which strongly affect the mechanical properties and therefore must be captured by any predictive modelling. One way to account for such effects is through detailed mesoscale modelling.

This study proposes a new 3D voxel-based mesostructure generator using a 3D random sequential absorption technique that incorporates bin-guided tape deposition, a tape draping method to produce waviness and resin pockets, and a control strategy for plate thickness variations. The numerical framework is fully integrated with finite element simulations to predict the elastic properties of thick, thin, and ultra-thin discontinuous composites via 3D computational homogenisation. A detailed statistical analysis is conducted to investigate the size of the statistical volume elements and the convergence of the elastic properties. In addition, microscopy analysis and nitric acid tests have been used to extract key modelling parameters for an ultra-thin discontinuous composite. Despite the uncertainties in the input properties of the tapes, the predicted results are in good agreement with the experimental values found in the literature. Finally, a comparison with equivalent laminate models is also provided. This illustrates the capabilities of the framework for potential applications requiring detailed 3D models such as material optimisation and damage studies.

ABSTRACT. Mean-field homogenization schemes, widely used to characterize the macroscopic behavior of composite materials, can be based on incremental processes. These methods are particularly relevant to estimate the effective characteristics of highly inclusionary media. Our study focuses on two incremental homogenization approaches: the so-called differential scheme [1,2] and iterative homogenization method [3]. These schemes gradually introduce different families of inclusions into an updated embedding medium. Our aim is to pursue a thorough comparison of these two models in various contexts, including anisotropic, multiphase media and different inclusion geometries (spherical, spheroidal, ellipsoidal).

On the one hand, the limit behavior of these two schemes for an infinite number of iterations is investigated analytically. In the case of isotropic two-phase media and spherical inclusion, Zimmerman estimates [2] are retrieved for both schemes. For more general cases, a criterion is proposed to determine a fittest number of intermediate media required to remain in the validity domain of the dilute distribution scheme used at each homogenization step. On the other hand, numerical simulations are performed to investigate the influence of the order of introduction of several inclusion families. These results are validated by comparisons with classical mean-field models and full-field FFT-based simulations.

[1] A. N. Norris, «A differential scheme for the effective moduli of composites», Mechanics of Materials, vol. 4, nᵒ 1, p. 1‑16, 1985. [2] R. W. Zimmerman, «Elastic moduli of a solid containing spherical inclusions», Mechanics of Materials, vol. 12, nᵒ 1, p. 17‑24, 1991. [3] R. Zouari, A. Benhamida and H. Dumontet, «A micromechanical iterative approach for the behavior of polydispersed composites», International Journal of Solids and Structures, vol. 45, nᵒ 11‑12, p. 3139‑3152, 2008.

ABSTRACT. Several mean-fields homogenization methods are readily available to estimate the effective properties of particulate composites, which account for the particles volume fraction, shapes and orientations. To also account for their spatial distribution, the Ponte-Castañeda and Willis (PCW) model [1] embeds a parametrization of the statistical distribution law, while the Interaction Direct Derivative (IDD) model [2] associates a matrix cell to each inclusion, representative of close interactions.

To calibrate and exploit these models, we propose a novel approach in the context of 2D linear conductivity when representative images of the microstructure are available. We discuss the links between the models [3] and the range of validity of the IDD model. When the IDD estimate lacks the necessary symmetry, both an IDD-based PCW model and a two-step scheme are proposed. Finally, an image analysis method using Voronoı̈ diagrams, inspired by a proposition of [2], is implemented to define the cells associated to each inclusion and supply the models.

The method is validated by comparisons between the obtained IDD and PCW estimates, the Mori-Tanaka (MT) model and benchmark full-field numerical simulations. Accounting for the inclusion distribution is seen to lead to better estimates, both qualitatively (by capturing anisotropic behaviors due to the sole distribution) and quantitatively.

[1] Ponte-Castañeda, P. & Willis, J. R. The effect of spatial distribution on the effective behavior of composite materials and cracked media JMPS, 1995

[2] Du, D. X. & Zheng, Q. S. A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of multiphase composites taking into account inclusion distribution Acta Mechanica, 2002

[3] Hessman, P. A.; Welschinger, F.; Hornberger, K. & Böhlke, T. On mean field homogenization schemes for short fiber reinforced composites: Unified formulation, application and benchmark IJSS, 2021

ABSTRACT. Fractional viscoelastic constitutive laws are expressed by differential equations involving derivative operators of non-integer order. This formalism allows to take into account long-memory effects that are experimentally observed in materials like polymers, ice or foams. In this talk, we address the homogenization of composite materials with such phases by means of an incremental variational approach. Specifically, we make use of the Effective Internal Variable (EIV) method, developed by Lahellec and Suquet, 2007. The EIV method was successfully applied to classical viscoelastic constituents (Tressou et. al., 2018), and is particularly attractive compared to the commonly used correspondence principle as it provides the fluctuations of the fields. This homogenization method relies on the Generalized Standard Materials framework in which the dissipative materials are entirely described by means of two convex thermodynamic potentials. Contrary to classical viscoelasticity, these thermodynamic potentials are not straigtforwardly expressed, but are obtained through the rheological interpretation of any fractional viscoelastic constituent as a generalized Maxwell model. We thus take advantage of the extension of the EIV method for several internal variables developed by Tressou et. al, 2023. Regarding the individual constituents, the distribution of the characteristic times is explicitely given by the expression of the fractional viscoelastic spectrum, thus they can be appropriately chosen by following the discretization procedure developed by Papoulia et. al, 2010. In order to consider fractional Zener constituents, we extend this discretization method to the Mittag-Leffler function. In this work, we consider a fractional Zener matrix reinfoced with elastic inclusions subject to a harmonic loading and compare our results with FFT-based computations.

ABSTRACT. The mechanical properties of short fibre-reinforced composites depend strongly on the injection moulding process. Due to its heterogeneous microstructure, fibre composite materials show not only a distinct anisotropy, but also spatially distributed viscoelastic properties on the component level. This is demonstrated experimentally at the macro level using tensile test specimens by investigating local deformation with a digital image correlation measurement system. Subsequently, on the micro level polished micrograph samples are used to investigate the entire cross-section by nanoindentation with a Berkovich tip. These experimental investigations show that the spatially distributed material properties are of stochastic nature and must therefore be considered in the modelling of short fibre-reinforced composites. A suitable modelling approach to describe the spatially distributed material properties in a 2D model are random fields, which are generated by utilizing the expansion optimal linear estimation method. This series expansion is based on a spectral decomposition of the correlation structure of the underlying microstructure. For modelling of the spatial distribution of material properties on the macro level using random fields, the information of the probabilistic characteristics of the microstructure, which given by probability density functions of fibre length, diameter and orientation are needed. These functions are obtained from the tensile test specimens by using computed tomography and are required for the generation of artificial microstructures. Subsequently, correlation structures are derived from the generated artificial structures for the generation of random fields. This approach allows the stochastic information of the fibre distribution to be considered in the modelling process. Since the microstructure depends, among other things, on the fibre content, this modelling approach is used for different fibre mass fraction. Finally, this modelling approach are compared with the experimental results.

ABSTRACT. The realisation of economically viable fusion reactors requires developing a full-scale “virtual reactor” representation of an operating tokamak device, informed by predictive materials models spanning the parameter space of simultaneous thermal, mechanical, and radiation loads. This work describes a combined in silico and in vivo study focused on quantifying deformation under stress and irradiation at low temperature.

While it is well known that irradiation accelerates creep deformation in metals, the phenomenon of irradiation creep becoming more pronounced at low temperature defies conventional understanding. In this talk, we will discuss the development of a virtual representation, or “digital shadow”, of the custom-designed “GIRAFFE” experiment for measuring stress-relaxation in a tensioned tungsten wire under irradiation. We show how atomic simulations can be used to generate a multiscale model capable of quantitatively predicting the elastoplastic response of a material under conditions of both stress and irradiation — ahead of the actual observation, without use of any adjustable parameters.

We discover that, under irradiation at room temperature, internal stresses of up to 2 GPa relax within minutes. As opposed to conventional notions of radiation creep, the effect arises from the self-organisation of nano-scale crystal defects, athermally coalescing into extended polarized dislocation networks that compensate and alleviate the external stress. The actively cooled materials, in which the stress concentrations critical to structural integrity are expected to form, would relax through the favourable low temperature creep mechanism explored in this study.

ABSTRACT. On the path towards nuclear fusion as a future energy source, the degradation of materials in structures and plasma-facing components represent a central challenge. These materials must withstand the harsh conditions of the fusion environment, such as high heat and particle fluxes of hydrogen and helium as well as intense irradiation by high-energy neutrons. It is known that the irradiation of metals using high-energy ions leads to accelerated creep, resulting in significant deformations. A detailed description of this effect has not yet been feasible due to the complexity of simulating such conditions in the laboratory.

For the experimental investigation of materials under such conditions, the General-Purpose Irradiated Fiber and Foil Experiment (GIRAFFE) was developed. A dedicated tensile testing machine that can perform mechanical testing under simultaneous irradiation with high-energy ions. Cold-drawn tungsten wire with a diameter of 16 µm was used as sample material to investigate the mechanical properties of tungsten under irradiation. This wire has a nano-scale microstructure, resulting in a large number of grains and grain boundaries in the irradiated volume, even at the low penetration depth of around 2 µm of 20.3 MeV W6+ ions. This makes the wire a suitable model system for describing polycrystalline tungsten.

Comprehensive irradiation induced stress relaxation experiments were performed by loading single 16 µm tungsten wires with an elastic tensile stress between 0.5 and 2.0 GPa while damaging them simultaneously up to a displacement damage of 5 dpa. During the experiment, the elongation of the sample is kept constant while the load drop is measured. Measurement of this load drop, caused by irradiation-induced stress relaxation, was enabled through a novel approach to in-situ investigations of the mechanical properties of materials during irradiation. The obtained data is thereby used for the validation of material models and for the engineering of fiber-reinforced composites.

ABSTRACT. The small punch test (SPT) is a miniaturized testing method used for determining thermo-mechanical material properties. In this method, a flat cylindrical sample (D8 x 0.5 mm) is centrally loaded by a punch featuring a spherical tip (R1.25 mm). The attractiveness of this approach, developed in the 1980s, lies in its simplicity and the minimal amount of material required. However, challenges arise due to the inhomogeneous stress and deformation state, complicating the determination of constitutive material parameters. To address this issue, an inverse approach is employed, utilizing finite element simulations of the SPT and nonlinear optimization methods to identify a parameter set that aligns the simulation results most closely with experimental findings. In the context of high-temperature small-punch creep tests conducted on the nickel-based superalloy 2.4842 (Alloy 699 XA), two strategies are employed to reduce test duration while preserving information quality. These include elevating test temperatures based on Larson and Miller's work, to achieve shorter failure times under equal forces. Additionally, the testing duration is limited to t=100h. Among the three applied loads, one is defined to induce specimen failure within 100 hours, while the others do not lead to specimen failure. The material model aims to predict the structural behavior of the nickel-based superalloy at high temperatures and is comprised of three components: linear isotropic elasticity, non-linear isotropic plasticity, and creep. The creep model represents a novel approach enabling the prediction of creep behavior across wide stress and temperature ranges. The identified creep parameters are largely independent of temperature and are suitable for extrapolation in terms of time and temperature, resulting in a much more realistic behavior compared to the commonly used Norton creep model.

ABSTRACT. Steels, tungsten and copper alloys are important in fusion engineering for structural, plasma-facing and cooling applications. They must withstand intense radiations that cause both volume swelling and irradiation-creep even at low temperature. Hence neutron transport calculations and materials modelling are two key ingredients of tokamak-scale structural simulations. The first provide the neutron fluxes and the second quantify their consequences. Irradiation produces microscopic defects in the metallic lattice, where the mismatch between the relaxation volumes of self-interstitials and vacancies gives rise to high stress concentrations in reactor components. Macroscopic swelling and dimensional changes stem also from the accumulation of nano-scale defects that gradually evolve into mesoscopic defect structures such as extended dislocation networks and vacancy clusters. This complex low-temperature evolution was simulated using molecular dynamics. Starting from the concept of the dipole tensor for an individual defect and introducing the density of relaxation volumes–which in the framework of elasticity is related to the general notion of eigenstrain– we outline and illustrate applications of a multi-scale approach to the evaluation of macroscopic stress and deformations arising due to irradiation at the component scale in a fusion power plant. The element- and alloy-specific density of relaxation volumes is derived from atomistic simulations or experiments, and it is directly implemented as a source of stress and strain in a finite element model, closing the length-scale gap. Alongside swelling, another technologically relevant radiation effect is the degradation of thermal conductivity of the metals, which is also directly taken from experiments in literature. We exemplify the two effects using fusion reactor components such as a breeding blanket module and an ITER divertor monoblock. We highlight how radiation-induced stresses arise primarily from the spatial variation of swelling, which can be caused by neutron exposure and/or temperature gradients. This is then up-scaled to full tokamak reactor simulations.

ABSTRACT. Screw dislocations are known to control strength of body-centered-cubic alloys. Interstitials such as C and N play a key role in the strengthening mechanisms. Yet, a mechanistic theory that enables the prediction of strength of alloys over a broad range of compositions and interstitial contents is not available. Here, we provide such a theory and apply it to screw dislocations with C and N in iron, from dilute to larger concentration. The theory, which accounts for interstitial solute segregation by Cottrell atmospheres, is validated with respect to atomistic simulations and used to predict the yield strength of a broad range of alloys, showing fully ferritic, martensitic and precipitation-strengthened microstructures. By using a recent model developed by the authors to predict the dislocation density of martensite as a function of the interstitials content, we find a new scaling of the yield strength with the dislocation density, which matches experiments and differs from the commonly used Taylor equation.

ABSTRACT. Tin alloy SAC305 is a popular lead-free solder since the phase out of Lead from consumer electronics about twenty years ago. Electronic cards are generally submitted to complex thermomechanical loadings inducing fatigue and/or creep damage. Numerous publications cover its mechanical behavior for a large range of testing conditions but results vary significantly from one author to another. SAC305 solder joints are typically constituted of 1-3 crystal orientations and failure has been found to be related to specific orientations. However, generally, only macroscopic polycrystalline characterization have been done on such Tin alloy. Rare characterizations have been conducted on SAC305 quasi-single crystals and with only very limited crystal orientations variations. In the same way, isotropic models are generally used for lifetime estimations, which limits the predictions done. In this study, SAC305 quasi-single crystal specimens have been obtained with a large variety of crystal orientations. Creep tests were conducted at 185°C on these specimens and the measured creep lives spread on almost 3 orders of magnitude depending on crystal orientations. From slip line analysis and digital image correlation during tests the activation of two slip system families was pointed out. Complementary, a crystal plasticity model implementing the identified slip systems reproduced well the deformation of the samples, the strain localization and the local rotation of the Tin crystal.

ABSTRACT. While exploring the principles of elastic fracture mechanics within a 3D architected solid, a captivating observation emerged. Elastic brittle architected solids demonstrated a distinctive rising R-curve, reminiscent of ductile solids, resulting in an unexpected enhancement of toughness in a typically brittle system. This revelation broadens the horizons of mechanics of architected solids to theories such as strain gradient elasticity. Notably, an architected solid displays a considerable size effect when subjected to substantial strain/stress gradients, showcasing a softening behaviour in contrast to the stiffening observed in continuum solids. Thorough investigations through large-scale numerical calculations and in-situ measurements, employing micro-tomography techniques, have unveiled this elusive micromechanical behaviour in mechanical metamaterials. These findings carry substantial implications for the design of solids featuring micro-architectures, especially in the context of structural applications.

ABSTRACT. Mechanical metamaterials deliver unconventional properties arising from their periodic architecture. Their functionalization offers opportunities for lightweight components in a wide range of applications where local toughening is of interest. While the advances in digital manufacturing unlock extraordinary design space, the poor understanding of the failure of metamaterials hinders their application to structural components. Moreover, a robust criterium for numerically predicting strut failure through architected materials with arbitrary cell geometry is currently lacking. Therefore, it is necessary to uncover the local failure mechanisms by in-situ characterization. In the presented work, we characterize the fracture behavior of 3D-printed polymer lattices under Mode I loading. We focus on unraveling the link between the local failure behavior of single struts and the work to fracture. We observe that, despite the brittle nature of the base resin, the cell tessellation introduces local non-linear effects, enabling higher work before catastrophic failure. In-situ imaging reveals distinct failure mechanisms, such as strut buckling or stress concentration at the lattice joints. Moreover, we quantitatively characterize the impact of the relative density on the failure energy of single-edge notched bend specimens. The direct monitoring of the breaking of individual struts will foster the development of robust failure criteria for 2D lattices. Overall, the outcomes of this work will guide the design of mechanical metamaterials with tunable crack propagation.

ABSTRACT. Selective laser sintering (SLS) has made possible the fabrication of lattice metamaterials, consisting of periodical structures with interconnected struts. However, SLS manufacturing originates porosity and surface roughness that critically affect the mechanical behavior of these structures due to their small diameters and high specific surface.

An experimental fracture analysis of unit cells and single struts of Polyamide12 has been made to analyze how the defects influence mechanical behavior and fracture of these materials.

In-situ compressive and tensile tests of unit cells and single struts of different diameters have been performed using X-ray tomography. Observations show that the behavior of both unit cell and strut material is less stiff than the one found in bulk samples. In the struts, the fracture occurs by crack nucleation in surface defects and its propagation, which depends mainly on the printing direction. In unit cells, on the other hand, crack nucleation and propagation is observed on the nodes that join at least a strut parallel to the applied force, which depends on geometry rather than defects.

This analysis is be complemented with a numerical analysis. The tomographies are used to generate voxelized geometries that include the actual strut shape, including the defects that originated during the printing process. These geometries are simulated using an FFT-based method, considering a phase-field fracture model.

ABSTRACT. Previous studies have consistently demonstrated that incorporating hierarchy into lattices can significantly enhance their mechanical properties. Many biological materials, known for their exceptional fracture toughness possess a hierarchical architecture. This work introduces hierarchy to three topologies (hexagonal, Kagome, and triangular) by incorporating a finer length scale triangular lattice. Our study quantifies the mode I fracture toughness through finite element simulations employing the boundary layer method. Additionally, analytical predictions are provided to explain the effect of hierarchy on fracture toughness. The findings indicate that hierarchy significantly improves the fracture toughness of bending-dominated lattices. The hierarchical hexagonal lattice exhibits superior fracture toughness compared to the simple hexagonal lattice. Notably, the fracture toughness of the hierarchical hexagonal lattice scales linearly with the relative density, while the fracture toughness of the simple hexagonal lattice scales as relative density squared. Stretching-dominated lattices did not benefit from introducing hierarchy. The numerical and analytical predictions were in good agreement, offering a comprehensive explanation of the advantages offered by a hierarchical design.

ABSTRACT. Hard-magnetic active elastomers consist of hard-magnetic particles embedded in a soft matrix. Their ability to rapidly and reversibly change the shape and properties under remote magnetic stimuli, makes them an attractive material platform for soft robotics, actuators and sensors, and biomedical devices. The research area has been witnessing explosive growth, driven by the development of material fabrication enabling the programming of intricate magnetization patterns in soft active materials. Recent studies include the exploration of shape-morphing, instability phenomenon, and achieving untethered actuation. However, despite these recent advances, a systematic understanding of their dynamic behaviors remains elusive, limiting their tremendous potential in nondestructive testing, energy harvesting, and smart soft wave devices.

Here, we put forward a novel design of Hard-magnetic Soft Metamaterials (HSMs) capable of active and remote manipulation of elastic waves, including the highly desirable broadband low-frequency wave attenuation, invisible cloaking, and solitary propagation. The metamaterial properties originate in their highly ordered microstructures that are fixed once designed and manufactured. Therefore, the active tunability of current metamaterials is limited. We utilize the complex magneto-mechanical coupling in highly ordered HSMs to break through the limitation in the metamaterial functions. The developed HSMs will open new levels of performance in applications ranging from broadband vibration isolation at challenging low-frequency ranges to robust energy harvesting with ultra-high transmission rates.

ABSTRACT. Magneto-active hydrogels (MAHs) consist of a soft polymeric network doped with magnetic particles that confer the ability to mechanically respond to external magnetic actuation. These multifunctional properties allow to control the material's state of deformation and its properties in a remote, dynamic and non-invasive manner. Taking advantage of this high degree of control of the mechanical properties of the hydrogel, the solvent diffusion dynamics between the MAH and the aqueous medium it is embedded within can be heavily affected and controlled. These characteristics, along with the low magnetic permeability of biological tissues and the good biocompatibility of hydrogels, make MAHs excellent for their application in the biomedical field as drug delivery vessels or for the collection of liquid samples from a localized region within the human body. However, the underlying physics of the magneto-mechanical-diffusion coupled problem are highly complex [1]. This work conceptualises new biocompatible MAHs from human blood plasma, with strong magneto-mechanical actuation. The material is experimentally tested using a technological in-house device to control different states of magnetic actuation [2]: controls with null actuating fields, sustained actuations under constant fields, and several modes of dynamic actuation at different modes and frequencies. This methodology enables an efficient and deep analysis of the diffusion process under magneto-mechanical actuation. In addition, we provide a new constitutive formulation and its implementation to model the diffusion process of two different species within a magneto-responsive material. The application of this mathematical model helps in understanding the underlying physical phenomena affecting diffusion dynamics. Taking together, the experimental and computational open new exciting opportunities for the use of ultra-soft (~100 Pa) MAHs in bioengineering applications.

1- D. Garcia-Gonzalez, C.M. Landis. Journal of the Mechanics and Physics of Solids, 139:103934, 2020.

2- M.A. Moreno-Mateos, J. Gonzalez-Rico, et al. Applied Materials Today, 27:101437, 2022.

ABSTRACT. Magnetorheological elastomers (MREs) are smart materials characterized by their modifiable mechanical and viscoelastic properties when subjected to a magnetic field. These materials are composed by magnetizable particles disperse within solid elastomer bases, aligning into chain-like structures during the curing phase.

Owing to their unique characteristics, MREs can be widely used in several aplication including the effective development of isolation and vibration reduction systems with tunable mechanical properties.

In this contribution, we will present an analytical formulation to describe a laminate structure comprising alternating layers of MREs and a passive yet stiffer material, such as an aluminum. The constitutive equation of the MRE is derived in the context of finite strain regimes, where an additional internal variable representing the elastic deformation of the matrix is used to account for the dissipative effects and is constitutively coupled with the external magnetic field. As a result, the elastic moduli and relaxation times are influenced by the external magnetic field. The response of the laminate structure is explored under forced oscillations.

The analytical framework provided in this context establishes a basis for comprehending and enhancing the performance of laminates based on MREs, providing valuable insights for their utilization in creating controllable semi-active damping systems.

ABSTRACT. Bioprinting is an advanced engineering procedure aiming at recreating a selected tissue by extruding a mixture of stem cells encapsulated in an external gel, named bio-ink, into a desired pattern. The transfer of the printed construct to a culture bath triggers cell differentiation and growth. However, prior to activating cellular processes, the gel must first be cured into a stiffer polymer construct to provide proper structural support for the cells. One of the most used techniques to achieve this is UV-induced polymerisation, whereby light interacts with the dispersed monomers in the construct and gradually transforms them into long, developed polymer chains. Many parameters regulate the interaction of the forming polymer with light: direction of incident light, exposure time, target value of the degree of conversion, the concentration of chemical species such as photo-initiators, monomers and oxygen to name a few. Since in many application fields the suitable choice of these parameters follows no standard protocols, this work intends to help in grounding their choice to a rational basis. To achieve this, the relevant Physics of what happens during the curing process is deposited has been represented through customized multiphysics Finite Element simulations, where the kinetics of polymer cross-linking has been coupled with finite deformation formulations.

ABSTRACT. Laser powder bed fusion (LPBF) additive manufacturing (AM) is gaining popularity as a versatile, pioneering and time-efficient method for manufacturing intricate parts directly from CAD designs, especially for biomedical applications such as stents or patient-specific orthopaedic implants [1]. However, given the wide range of AM process variables and complex melting/solidification histories, defects and porosity are almost inevitable, which in turn affect the integrity and mechanical performance of produced parts [2]. This modelling study establishes a process-structure-property (PSP) relationship for additive manufacturing of AISI 316L specimens. The methodology is based on a new geometrically-based rationale for the selection of AM process variables (hatch spacing, layer thickness and laser energy density), combined with crystal plasticity finite element (CPFE) micromechanical models that include melt pool microstructural morphology, texture and porosity. The effects of AM process variables and porosity on ductility, yield strength and UTS are analysed. The new methodology has allowed identification of optimal hatch spacing and layer thickness for a given laser spot size, power and scanning speed. Moreover, CPFE modelling reveals the detrimental effect of porosity on the ductility and strength of the struts.

ABSTRACT. Additively manufactured (AM) components exhibit distinct microstructures compared to conventionally manufactured ones, primarily due to unique thermal histories at the local level during the build process. Prior studies demonstrated notable variations in the mechanical properties of AM thin-walled structures (TWS) in response to changes in wall thickness, with this variability being temperature-dependent and is more pronounced at elevated temperatures. In this research, the nature of this size effect on tensile properties, including yield strength, strain hardening rate, and ductility, for AM-HAYNES 214 at elevated temperature (250°C and 450°C) is studied. To explore the size effect, TWS were fabricated with four different thicknesses: 1mm, 1.5mm, 2mm, and 2.5mm. To derive the constitutive response, we developed a robust approach using electron backscattered diffraction (EBSD) images of sections to generate distributions of morphological and crystallographic parameters, including grain sizes, texture, and twin fraction. The methodology's effectiveness is validated by comparing simulated microstructure statistics with real EBSD data. Subsequently, we employed the Crystal Plasticity Fast Fourier Transform (CPFFT) based spectral method, relying on a phenomenological hardening law. We successfully established a correlation between the local stress analysis conducted at the grain level and the global mechanical behavior observed in experimental results. This comprehensive examination of stress and strain at the micro level has uncovered variations in mechanical properties that are directly linked to the thickness of the AM-TWS. Additionally, we explored how the local stress state, influenced by grain neighborhood effects, contributes to the observed localization behavior. We explored factors that drive the non-uniform distribution of mechanical responses by addressing how the local stress state, influenced by these grain neighborhood effects, contributes to localization behavior. The study's discovery of manufacturing-induced plastic anisotropy in grain distribution presents research opportunities. It enables the optimization of grain topology and solidification parameters, enhancing the mechanical behavior of AM-TWS.

ABSTRACT. Binder Jetting (BJ) is an advanced additive manufacturing technology which allows the production of intricate metal components. The resulting part consists of a mixture of thermoplastic binder and metal powder, requiring further steps of debinding and presureless sintering of the green part. In the sintering stage, part densification involves both shrinkage and distortion. This paper introduces an elastic-viscoplastic model that accounts for the macroscopic deformation behaviour in the sintering process of 17/4PH steel parts produced through BJ. The model addresses the problem by considering a viscoplasticity model that depends on the first and second invariants of the stress tensor and an effective sintering stress that mimics the shrinkage due to diffusional mechanisms involved in the sintering process. The parameters arising in the formulation were identified through a calibration procedure involving an experimental campaign including dilatometry tests. The model, implemented in finite element software, has demonstrated its capability to reproduce the macroscopic deformation behaviour of 17/4PH steel parts obtained through BJ, encompassing different geometries.

ABSTRACT. The prediction of part distortion and component-level residual stresses in additive manufacturing (AM) is of high priority as the community seeks to increase part complexity and size. As-built stress-state predictions are particularly challenging for metal-based AM because many of the material models previously developed were not intended for the cyclic and heterogeneous heating present during the AM process. Additionally, accurate representation of the thermal history requires the use of a moving heat source and material deposition, both of which add significant computational expense. This work examines the influence of material model choice in thermo-mechanical finite element (FE) simulations of the directed energy deposition (DED) process of Ti-6Al-4V components. Specific emphasis will be placed on distortion and as-built residual stress predictions from the various material models. The Evolving Microstructural Model of Inelasticity (EMMI) internal state variable (ISV) model and an elastic-perfectly plastic (EPP) model were selected for comparison. EMMI is a physically-based strain rate- and temperature-dependent dislocation mechanics-based ISV plasticity model that was previously developed for FE simulations of welding; it has been adopted in this work for use with the metal-based DED process. The thermal model calibration procedure will also be examined to determine its effect on mechanical response. Results show significant differences predicted in the stress evolution and overall stress contour across the part despite similar maximum von Mises stress.

ABSTRACT. In the scope of understanding the factors controlling the defects that commonly appear in the microstructures of materials produced by Additive Manufacturing (AM), a first step is the prediction of the thermal history at which the material is subjected by means of different printing parameters. The extremely large amount of different combinations of printing parameters (laser power, hatch distance, laser scanning speed…) adds to the different printing geometries which also can vary the influence of such printing parameters. Its computation by means of Finite Element Modelling is the logical choice, but is time consuming and cannot be used in large computational optimization processes.

This work therefore aims at developing a fast and accurate predictive methodology to calculate temperature history at during the AM process. First, a Finite Element Method (FEM) model was developed to extract thermal profiles at key points for Selective Laser Melting processes, optimized for computational efficiency for more than 3000 different printing parameters combinations. Subsequently, different Machine Learning (ML) methodologies are tested as predictive models to determine the most robust approach. The models employed include XGBoost, Random Forest, Extremely Randomized Trees (ERT), and Feedforward Neural Networks (FNN). These models were fed with the dataset, yielding optimal predictive outcomes for both ERT and FNN with very good performance. It demonstrates that it is viable to develop models based on ML for predicting thermal profiles in AM using as input the printing parameters. It also determines the performance difference among several of the ML models. This has led finally to a predictive model that offers quasi-instantaneous predictions with minimum error as compared to the computationally expensive FEM simulations.

ABSTRACT. In this work, we explore rate-dependent instabilities in visco-hyperelastic periodic composites through post-buckling analysis. Our investigation into the influence of loading strain rate on critical strain and wavenumber integrates numerical simulations and analytical predictions. Analytical estimates for critical strain in visco-hyperelastic laminates are developed, considering the interplay between fiber-to-matrix stress contrast. These analytical results align well with numerical simulations, validating the reliability of our proposed estimates. Our findings demonstrate a relationship between critical strain and strain rate, indicating a consistent decrease in critical strain with increasing strain rate. This rate-dependent behavior is characterized by distinct bounds for fast and slow loading rates. Furthermore, we observe that the critical wavenumber of laminates with lower fiber volume fractions decreases from a finite value to almost zero as the strain rate increases. In contrast, laminates with higher fiber volume fractions maintain a nearly zero critical wavenumber, irrespective of the strain rate.

ABSTRACT. We investigate instability-induced patterns in soft particulate composites under finite strains. Soft material can exhibit stiffening at finite deformations. In turn, this material nonlinearity influences the elastic instabilities and the subsequent development of buckling patterns. In our study, we employ the Gent model to analyze and illustrate the behaviour of soft particulate composites. This model uses a single locking parameter (Jm) to adjust the stiffness of the soft material. We illustrate how the inhomogeneous deformation, together with the deformation-induced stiffening of the matrix, influences the instability characteristics, such as critical wavelength and critical strain. The inhomogeneous deformation gives rise to two particulate systems, resulting in stabilization at lower aspect ratios. Notably, we observe that this stabilization becomes more significant with variation in stiffness.

With higher Jm values, the composite’s behaviour closely aligns with the neo-Hookean model. Conversely, a decrease in Jm leads to earlier buckling, especially at larger aspect ratios, while interestingly, for lower aspect ratios, this buckling occurs later than in the case of larger aspect ratios. Furthermore, we find that the stabilization effect for lower aspect ratios becomes more prominent with lower values of Jm. Finally, our results reveal that the material stiffening, associated with decreasing Jm, does not consistently lead to earlier buckling due to the influence of nonlinearity in the strain field.

ABSTRACT. In this contribution we present a numerical model that can describe the pore formation/cavitation in viscoelastic food materials during dry- ing. The food material has been idealized as a spherical object, with core/shell structure and a central gas-filled cavity. The shell represents a skin as present in fruits/vegetables, having a higher elastic modulus than the tissue, which we approximate as a hydrogel. The gas-filled pore is in equilibrium with the core hydrogel material, and it represents pores in food tissue as present in intercellular junctions. The presence of a rigid skin is a known prerequisite for cavitation (inflation of the pore) during drying.

For the modelling we follow the framework of Suo and coworkers, describing the inhomogeneous large deformation of soft materials like hydrogel - where stresses couple back to moisture transport. In this paper we have extended such models with energy transport, and viscoelasticity - as foods are viscoelastic materials, which are commonly heated during their drying.

To approach the realistic properties of food materials we have made viscoelastic relaxation times a function of Tg/T , the ratio of (moisture dependent) glass transition temperature (Tg) and actual product temperature (T). We clearly show that pore inflation only occurs if the skin gets into the glassy state, as has been observed during the (spray) drying of droplets of soft materials like foods.

ABSTRACT. Synthetic polyvinyl alcohol (PVA) hydrogels are interesting materials as substitutes for the reconstruction of soft tissues due to their biocompatibility and adjustable mechanical properties. In particular, their tensile response can be enhanced by orienting their semi-crystalline network. Assemblies of such anisotropic PVA hydrogel fibers were shown to reproduce the water content, dimensions, and tensile response of the human ligament. Here, we investigate the role of the network anisotropy in the mechanical response of PVA hydrogels. For that, we compare anisotropic PVA hydrogel fibers to isotropic PVA hydrogel films having similar crystallinity (50 ± 2%) and swelling ratio (2.5 ± 0.2). Uniaxial tensile tests were performed on single fibers and films in water at 20°C and 37°C. Both systems exhibited very different non-linear viscoelastic behaviors. For low tensile strains (0-20%), anisotropic hydrogel fibers were significantly stiffer than isotropic hydrogel films, with Young’s moduli of 13.5 ± 2.5 MPa and 2.7 ± 0.3 MPa, respectively. For large strains, the tensile responses differed even more. The isotropic hydrogel films softened considerably above 50% strain with a high elongation at break of 300% and tensile strength of 2.8 ± 0.4 MPa. On the contrary, the anisotropic hydrogel fibers exhibited a marked non-linear stiffening similar to that of biological tissues with a tensile modulus increasing up to 40 MPa and tensile strength values (20-30 MPa) close to those of human ligaments (20-40 MPa). Moreover, cyclic loading tests show that individual fibers undergo a softening after the first cycle but fully recover their pristine behavior after a few hours rest. These softening and self-recovery are well explained by the dissociation and reformation of reversible hydrogen-bonds in the swollen phase of the hydrogel. Such fibers constitute promising building blocks to design durable tissue substitutes able to sustain physiological fatigue loadings representative of ligament biomechanics.

ABSTRACT. Hydrogels are hydrophilic polymers keen to uptake a large amount of water within their molecular network. Thanks to their physical, chemical, and mechanical properties close to those of biological matters and tunable in a wide range of values, hydrogels can be conveniently employed in a variety of fields, ranging from soft robots to biomedical applications [1]. Mechanical properties of gels are strictly related to the amount of water present in their network, and it has been recognized that – among others – the gel’s elastic modulus usually decreases with the degree of swelling. In the present paper, we experimentally investigate the swelling degree-hydrogel stiffness relationship. It is experimentally observed the unexpected swelling-induced stiffening for extremely high water contents. A physics-based theoretical model considering: (1) the dissociation of intermolecular hydrogen bonds (which results in a decrease in chain density and an increase in the contour length of the chains) [2], and (2) swelling leading to the stretching of the chains [3] to accommodate additional water molecules, is proposed to justify the observed behavior. This finding opens new perspectives in obtaining gels whose stiffness can be made to vary by tuning the water content. This can be achieved, for example, by varying the temperature in temperature-sensitive hydrogels.

References [1] Flory, P. J. (1942) Thermodynamics of high polymer solutions. The Journal of chemical [2] Cohen, N., and Eisenbach, C. D. (2019) A microscopically motivated model for the swelling-induced drastic softening of hydrogen-bond dominated biopolymer networks. Acta Biomaterialia 96, 303 – 309. [3] Kuhn, W., and Grun, F. (1942) Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe. Kolloid-Zeitschrift 101, 248–271.

ABSTRACT. When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and polymer gels are often porous, and can be permeable to the surrounding fluid. In particular, poly-N-isopropylacrylamide (PNIPAM) hydrogels swell by a few hundred percents in thickness when brought into contact with a solvent. Here, we present Surface Forces Apparatus (SFA) experiments, in sphere-on-flat mode, performed on initially fully swollen PNIPAM nanometric films. Together with modelling efforts, the progressive approach and indentation of the gel enables to highlight a succession of several different mechanical responses. From a regime with no gel-probe interaction, the hydrogel first undergoes a gentle deformation of its surface in a lubricated regime. Then, the indentation of the probe in a contact regime forces the expulsion of the solvent from the polymer matrix. We finally show that, at room temperature, the imposed mechanical load triggers the dehydration-induced glass transition of the PNIPAM. Our results are relevant in the context of biomimetic systems and/or living systems, that exhibit complex and different responses depending on the stimulation conditions, such as cartilages or biological membranes.

ABSTRACT. When cracks propagate, either quasi-statically or dynamically, they may deflect from its original plane or bifurcate into several branches. Both deflected and branched cracks are of engineering significance, as epitomized by hydraulic fracture or crack extension in heterogeneous media. In this talk, we may cover several aspects pertinent with deflected or bifurcated cracks. 1, A close-form crack deflection criterion: when G_w/G_0≤cos^4 (α/2), the crack deflects into the weak plane with the critical energy release rate G_w, and that for straight crack propagation is G_0, α is the deflecting angle. This equation supplies a simple yet elegant criterion for the transition of a straight crack deflecting into a weak plane. 2, The elastic field of kinked cracks of arbitrary size. By adopting the Schwartz-Christoffel conformal mapping and the Muskhelishvili theory, we supplied a general way to solve the elasticity problem of cracks with complicated geometries, for both kinked and branched cracks. 3, The elasticity of a cracked half-plane with two typical scenarios: a double branched crack with two rays emanating from one point on the edge and two edge cracks spaced by a certain distance. Typical loading conditions are considered, including far-field uniform tensile stress and concentrated loads along either the tangential or the normal direction of the free surface. The talk includes a semi-analytic solution to those boundary-value problems in the cracked half-plane.

ABSTRACT. Remarkable mechanical properties have been reported in recent literature [1] for CoCrFeMnNi-based high entropy alloys (HEAs), making these HEAs potentially attractive candidates for future cryogenic applications. However, the damage and fracture behavior of HEAs has not yet been fully explored, especially at low temperature.

The present study evaluates the plane-stress fracture resistance of CrMnFeCoNi and CrCoNi alloys at room and cryogenic temperatures using the essential work of fracture (EWF) method. The EWF approach is a well-adapted method for simple and efficient characterization of the fracture resistance of thin sheets made of ductile materials

Stainless steels are found to exhibit an outstanding low-temperature fracture energy, reaching up to 2500 kJ/m^2, surpassing the 700 kJ/m^2 determined for HEAs. A predictive model was developed and validated experimentally in order to connect the thin sheet fracture toughness to the strain hardening capacity through separating the necking and damage work spent in the fracture process zone [2]. The insights gained from this study offer valuable guidelines for refining and optimizing metallic alloys further.

[1] Laplanche, G., et al. "Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi." Acta Materialia 128 (2017): 292-303. [2] Hilhorst, Antoine, Pascal J. Jacques, and Thomas Pardoen. "Towards the best strength, ductility, and toughness combination: High entropy alloys are excellent, stainless steels are exceptional." Acta Materialia 260 (2023): 119280.

ABSTRACT. In crystalline materials, fracture is often coupled with plastic activity. A comprehensive mesoscale modeling of fracture should therefore incorporate crack propagation and its interplay with dislocation multiplication and glide.

Both cracks and dislocations are associated with discontinuities in the displacement field. Therefore, it should be possible to construct a model based only on the displacement field. This requires the identification of a nonlinear elastic energy functional that is invariant with respect to the point group of the lattice, but also with respect to any shear deformation that leaves the lattice invariant.

In this talk, we show how to construct this infinitely degenerate potential energy and discuss the numerical implementation of the model. Finally, we present simulation results that reproduce the nucleation and propagation of dislocations in a potentially cracked crystalline system.

ABSTRACT. Predicting fatigue failures remains one of the most elusive challenges for scientists and engineers. In this work, we develop a comprehensive phase field model capable of predicting fatigue failures of arbitrary complexity. Through comparison with experiments, the model is shown to accurately predict the fatigue behaviour of materials, including S-N curves, Paris law crack growth, the influence of the load ratio, mean stress effects, stress concentrator factors and the endurance limit. In brittle and quasi-brittle solids, the model is able to predict fatigue crack growth rates from S-N curves, and vice-versa. Moreover, the framework is extended to account for the presence of hydrogen, which is known to significantly impact the fatigue resistance of metals. The resulting coupled deformation-diffusion-damage model is shown to be able to qualitatively and quantitatively capture the role of hydrogen in increasing fatigue crack growth rates and decreasing the number of cycles to failure. Our numerical experiments enable mapping the three loading frequency regimes and naturally recover Paris law behavior for various hydrogen concentrations. In addition, Virtual S–N curves are obtained for both notched and smooth samples, exhibiting a good agreement with experiments. Aspects of the numerical implementation will also be discussed, showing how complex fatigue cracking phenomena in 2D and 3D can be captured, over millions of cycles, through the development and use of new acceleration schemes.

ABSTRACT. Titanium alloys are increasingly used in aircraft engines. Ti components experience elevated temperatures of up to 550°C in oxygen-containing environments. Quasi-alpha Ti alloys are particularly prone to oxygen ingress, exhibiting up to 33% at. O, making oxygen-induced embrittlement a major concern for its deployment to higher temperatures. This work aims to improve the understanding of the interplay between oxidation induced embrittlement, aging and microstructural effects on fatigue life of quasi-alpha titanium alloys. We focus on a forged Ti6242S commercial alloy commonly used in aircraft engines. Two bimodal microstructures of high/low lamellar colonies surface fraction are studied in their reference state as well as after oxidation at 600°C for 3000 hours. Pre-oxidation led to the formation of an ~80 µm oxygen-enriched layer, characterized by SEM-WDS. Tensile properties and fatigue life were investigated through mechanical testing at room temperature and 550°C, SEM-fractography and TEM-FIB dislocation networks analysis. Tensile tests did not show any detrimental effect of oxygen-ingress on fracture strain at 550°C. Fatigue life was found to be mainly driven by crack initiation. At both ambient temperature and 550°C, both the pre-oxidation and the fraction of lamellar colonies exhibited a significant influence on fatigue life. At room temperature, pre-oxidized samples exhibited a stress threshold phenomenon, with no observable O-induced embrittlement on fatigue life below approximately 650 MPa and a drastic decrease in fatigue life at higher stress amplitudes.

ABSTRACT. In the present study, stress-controlled fatigue is carried out on SS316L at room temperature and -80 ℃ to understand its ratcheting behaviour. Two sets of tests were conducted, i.e. keeping stress amplitude constant and keeping mean stress constant. Plastic strain accumulation was observed in all the tests. However, there was a steady increase in plastic strain accumulation at room temperature, but an increase followed by a saturation of plastic strain was observed at -80 ℃. This saturation can be attributed to strain-induced martensitic transformation (SIMT) which was confirmed with the help of X-ray diffraction methodology. At maximum mean stress as well as maximum stress amplitude, the damage initiation started too early for any SIMT to take place, hence the saturation in plastic strain is not observed at those stress levels.

ABSTRACT. Understanding the impact of reactor load and environment on the Zr weld joint is one of the key factors to the structural integrity of light water reactors. New mechanistic modelling has been established by incorporating thermal recovery of loop dislocations and temperature-dependent loop-dislocation interactions to capturing the tensile behaviours of pre-irradiated Zr samples under thermal conditions. A critical bending test is set up for welded microstructure with notch embedded under thermo-mechanical cycles within reactor conditions. Accordingly, multi-scale modelling of high-fidelity weld is performed by incorporating real-time bending stresses (normal and shear) onto the local welded microstructure from EBSD scan, which captures the post-cycle and post-thermal material strengths. At potential crack nucleation sites identified by stored energy density, non- and pre-irradiated cases show completely different historical change. The synergy between thermal recovery and channel clearing is argued to be the main driver for creep fatigue initiation.

ABSTRACT. The 316L stainless steel produced by Laser Powder Bed Fusion (LPBF) demonstrates excellent resistance to pitting corrosion compared to conventional 316L stainless steel, with comparable fatigue strength. Nevertheless, its fatigue performance remains highly dependent on manufacturing parameters. However, few studies have focused on the coupling of these two phenomena, as occurs during corrosion fatigue tests. The main objective of this work is to study the interactions that take place between the cyclic loading applied, the microstructure of the material and the corrosion mechanisms involved in these tests. Firstly, heat treatments were applied in order to modify the microstructure of LPBF 316L on several scales. Each microstructure obtained was then characterised. Corrosion tests conducted in a solution containing 0.6 M NaCl were used to investigate the different electrochemical interactions of each metallurgical state with the environment. Secondly, uniaxial high cycle fatigue tests (1e6 cycles) were carried out in air and in a solution containing 0.6 M NaCl with a loading ratio R = 0.1. The electrochemical behaviour of the passive film was studied during the corrosion fatigue tests by monitoring the open circuit potential (OCP) and performing electrochemical impedance spectroscopy (EIS) measurements. The corrosion fatigue crack initiation was related to the passive film strength under cyclic loading and the presence of additive manufacturing process defects. Through in-situ electrochemical measurements, a decrease in the OCP has been observed in correlation with crack propagation. Subsequently, a specific number of cycles associated with this propagation was determined. Based on these results, the Paris law parameters were calibrated. These results have enabled us to identify the role of heat treatment on the corrosion fatigue crack initiation and propagation in LPBF 316L.

ABSTRACT. The so-called mechano-diffusion theory can describe many different phenomena dealing with a solid matrix swollen with a liquid; in particular, it describes the effects of liquid uptake or release, called swelling and drying, respectively.

We present a unified approach to set and solve mechano-diffusion problems where the solid matrix is made of two or more materials having different elastic and chemical properties. The amount of liquid that can be absorbed by the solid matrix depends on the chemo-mehanical properties of the material, and there are uncountable examples of swollen solids made of very different materials, having an almost steady and stress-free configuration; however, these free-swollen configurations will become stressed and distorted upon any change of liquid content because of swelling incompatibility.

The approach presented here is based on the theory of nonlinear mechanics with large distortions, coupled with that of swelling, describing the effects of solvent uptake in a solid matrix. Basing on the hypotheses underlying the two theories, and using some key principles of continuum mechanics, we present a chemo-mechanical model which describes the effects of swelling for materials made of domains having different properties

We presents some examples of gels having a hard skin surroundig a soft core; the geometry and the materials properties might yield noticeable shape changes during wetting or drying.

ABSTRACT. Hydrolytic degradation is a common degradation mechanism in biodegradable hydrogels used in biomedical applications such as tissue engineering and drug delivery. Hydrolysis causes the cleavage of chains in the polymer network, leading to a reduction in elasticity and swelling, as well as to mass loss. Recently, hydrolysis-assisted cracking has also been identified as a possible reason why cracks can propagate in rubber networks under small loads. The reaction kinetics is enhanced by the force experienced by the chains, and since the stress field is amplified around the crack tip, chains in that region are more prone to cleave than in the bulk. However, there have been limited attempts at developing comprehensive constitutive models that couple the effects of stress and hydrolytic degradation in rubbery networks. Specific challenges include capturing the effect of degradation on the elastic properties, and the force-dependent kinetics of chain scission. Ideally, models should also account for the architecture of the underlying polymer network, which ultimately dictates the macroscopic properties. In this work, we combine a Discrete Network (DN) model of rubbery elasticity with a stochastic degradation model based on the Kinetic Monte Carlo method to explicitly account for the evolving network structure and force-dependent hydrolysis. We illustrate the capability of the model by simulating degradation under free and constrained conditions. Our results show that force-dependent kinetics significantly impacts the degradation response, and that it can induce anisotropy. Using the results of the DN model as reference, we also develop a simplified mean-field continuum model able to reproduce the key trends of the DN model. The continuum model is suited for large-scale finite-element simulations coupling large deformations and the transport of water and reaction products.

ABSTRACT. Semi-permeable membranes are porous materials/structures that have several applications in different industries and daily life, for example as a key component in osmotic filtration systems. To date, fluid dynamics and osmotic mass transfer in membrane-bounded channels has been investigated mostly assuming undeformed configurations. However, many osmotic membrane processes, including Reverse Osmosis (RO) and Pressure-Retarded Osmosis (PRO), may undergo high-pressure conditions that cause significant membrane deformations due to pressure differences between the fluid channels. On the other hand, the deformations can change membrane channel spacing and configuration which have a great impact on both bulk flow conditions (pressure, velocity, etc.) and the osmotic-driven mass transfer through the membrane. To study such effects, a multi-physics computational model is implemented in this work, coupling a CFD solver (for fluid dynamics), a FSI model (for fluid-structure interactions) and mass transfer models (for osmotic transmembrane flow). The obtained results for a flat sheet membrane show that the hydrodynamics in the fluid-filled channels of membrane has significant impact on several process aspects, such as the pressure drop and osmotic fluxes. It is observed that alteration of the fluid velocity/pressure profiles and External Concentration Polarization (ECP) in adjacent deformed channels may lead to considerable change in transmembrane flux and Internal Concentration Polarization (ICP) values. This effect is most critical for the case that we use a high-pressure solution (deforming the membrane towards the low-pressure side) as the draw solution with high concentration of solute (strong ECP effect), a typical configuration in the PRO systems. It can be concluded that membrane deformations and flow redistribution effects may become even larger for thinner membranes or higher working pressures, where the use of meshes/spacers is inevitable. Therefore, process modelling and optimization tools are necessary for compromising between the structural stability of the membrane and the osmotic-driven mass transfer performance.

ABSTRACT. Composites made of liquid crystal (LC) inclusions embedded into a stiff polymer matrix have long been developed for engineering applications, such as switchable windows and smart screens for light shuttering and energy preserving purposes. Recently, LC inclusions have also been incorporated into soft matrices, such as hydrogels, for applications like artificial tissues and biosensors. For example, ultrasensitive flexible sensors are designed to detect weak mechanical stimulus. Loadings on such sensors can trigger the reorientation of the LC molecules and alters the electronic characteristics of the composite, which accurately measures the load. Understanding the behaviour of such systems requires an accurate description of the various physics involved, including the elasticity of the LC inclusions and the soft matrix, and surface tension.

In this work, we have developed a continuum mechanics formulation for a hyperelastic matrix reinforced with (nematic) LC inclusions. The elastic energy of the inclusions, attributed to the distortion of the director field, is described using Landau-de Gennes theory. Anchoring effects at the inclusion-matrix interface are described through anisotropic surface tension. We have implemented our continuum theory in the finite element code FEniCSx to investigate the role of various material parameters (anchoring strength, distortion elastic constants, volume fraction) on the effective properties of the composite. We show that the LC inclusions can stiffen the composite, and further that the stiffening depends on the loading direction relative to the LC director field. This is attributed to interfacial effects, which mediate the interactions between matrix deformation and reorientation of the LC molecules. The theory is further generalised to describe the effect of applied electro-magnetic fields. Our results contribute to a better understanding of the stimuli-responsive properties of polymer dispersed liquid crystals and provide useful insights for material design.

ABSTRACT. Through pregnancy, the cervix, a collagenous and hydrated tissue, undergoes a remarkable transformation from a rigid/closed structure that keeps the fetus inside the uterus to a more compliant/extensible one that opens to facilitate delivery at parturition. This process, known as cervical remodeling, involves complex changes in the cervix's equilibrium and dynamic mechanical properties, such as stiffness, viscoelasticity, and permeability. Constitutive models of the cervix extracellular matrix (ECM) calibrated with experimental data at equilibrium and obtained from animal cervical tissue, mostly rodents, have proven helpful in studying how the cervix softens through gestation. Recently, a poro-viscoelastic model of the human cervix was used to describe the human cervix's time-dependent behavior but limited to compressive strains and two gestational points (pregnant and nonpregnant). Building upon these previous constitutive models, we implemented a nonlinear anisotropic viscoelastic model of the cervix ECM, which captures the poro-visco-elastic behavior of the cervix under both compressive and tensile deformation. To calibrate our model, we used force-displacement experimental data from spherical indentation and uniaxial tension tests in cervix samples from Rhesus macaques, chosen because of their homology to humans, and collected at four relevant gestational time points. We observed that different mechanisms dominate the viscoelastic response of the cervix depending on the state of stresses and gestational time point. Under compressive load, as it occurs in indentation tests, the cervix's dynamic behavior is dominated by interstitial fluid flow through the porous cervix ECM. In contrast, in the case of uniaxial tension, the arrangement of the collagen network and interactions with other ECM components, such as proteoglycans, play a more critical role. This work gives insights into normal cervical remodeling, which is crucial to developing diagnostic methods and treatments for conditions such as cervical insufficiency, which is known to lead to preterm birth (birth before 37 weeks).

ABSTRACT. Fibrous materials may undergo an internal reorganization, which turns out in the emergence of preferential directions. This is a peculiar behavior of many biological tissues, which drive reorientation by external stimuli at chemo-mechanical levels. In particular, it is detected that contractile cells can reorganize fibrous extracellular matrices and form dense tracts of aligned fibers (tethers), that guide the development of tubular tissue structures and may provide paths for the invasion of cancer cells. Tether formation is caused by buckling instability of network fibres under cell-induced compression. We present a simple mechanical model within a variational framework that captures the essential aspects of these phenomena. The model qualitatively describes: (i) the emergence, induced by local compressive strain, of anisotropy, where fibrous materials exhibit directional preferences; (ii) the occurrence of micro-buckling, which leaves a lasting plastic deformation in the material; and (iii) the formation of localized field patterns, which contribute to the overall behavior of the material. By considering these fundamental aspects, our model provides insights into the mechanical response of fibrous materials and sheds light on the underlying mechanisms driving their behavior.

ABSTRACT. Due to the fact that fibers in soft tissues can usually carry less compressive loadings, a tension-compression asymmetry is observed in the experiments. Unfortunately, it is not easy to determine the correct material model for such phenomena, especially when inelasticity is involved. Therefore, the inelastic Constitutive Artificial Neural Networks (iCANNs) presented in [1] can be used to overcome this problem. iCANNs provide a new framework for model finding that extends Constitutive Artificial Neural Networks (see [2]) to general inelastic material behavior. It assumes a multiplicative decomposition of the deformation gradient and is therefore able to capture finite deformations and deformation rates. The overall design of the iCANNs provides a priori thermodynamic consistency, objectivity, rigid motion of the reference configuration and independence of the rotational non-uniqueness. The network architecture combines a recurrent neural network with two individual feed-forward networks for the Helmholtz free energy and the pseudo potential. Since our focus here is to discover a model for tension-compression asymmetry in plant tissues, we first extend iCANNs further by multiplicatively decomposing the deformation tensor into positive and negative parts, and second, we assume an additive split of the isochoric part of Helmholtz free energy into positive and negative parts. We train the iCANNs on cyclic uniaxial stress-relaxation experiments for petiole of Stephania japonica, in order to find the material model describing the desired physical phenomenon. Furthermore, we present performance tests of the iCANNs on other data sets and discuss the accuracy of our approach.

REFERENCES [1] Holthusen, H.; Lamm, L.; Brepols, T.; Reese, S.; Kuhl, E. Theory and implementation of inelastic Constitutive Artificial Neural Networks. Computer Methods in Applied Mechanics and Engineering. (2023). DOI:10.48550/arXiv.2311.06380 [2] Linka, K.; Kuhl, E. A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering. (2023) 403:115731. DOI:10.1016/j.cma.2022.115731

ABSTRACT. Granular materials are systems for which describing mechanical properties poses a major challenge due to the complexity of their amorphous structure. The lack of knowledge on the nature of the elementary mechanisms responsible for plasticity makes the understanding of how they deform a daunting task. It is nevertheless essential to better predict landslides and earthquakes. Advanced characterization approaches, such as optics and X-ray tomography, offer the possibility to study deformation at the scale of the particle but are hampered by their complexity and long acquisition times. Characterizing the deformation of granular materials is challenging, particularly in sudden phenomena such as avalanches. In this context, scattering methods may provide complementary information to scanning methods. Namely, acoustic waves benefit from long propagation distances and are able to effectively probe in the bulk systems such as granular suspensions. Here, we study a dense granular suspension in the elastoplastic regime, inserted in a rotating drum oscillating at angles inferior to the angle of repose. To probe the structure of the suspension, some ultrasound pulses are emitted from one side of the drum and the transmitted signal is collected at the other side. Experimentally, the granular suspension compacts, leading to rearrangements of grains and modifications of transmitted ultrasound signals. In order to measure strain, we propose a new method based on the correlation of transmitted multiply scattered ultrasound waves, sensitive to volumetric deformation of 10^-5. The method can detect local strain at the scale of a few grains and can therefore be applied in systems with heterogeneous deformations.

ABSTRACT. Relationship between the microstructure of secondary phases and the mechanical performance of metastable β −Ti - alloys is currently an intensively studied topic. Even very small changes in volume fractions of secondary phase particles have a measurable effect on the elastic constants of the dual-phase material. This effect is particularly pronounced for the softest shear elastic constant C´, that stiffens two times between the solution-treated material and a material with approximately 60% of ω particles for Ti15Mo. We present the capability of ultrasonic methods to assess the effective crystal symmetry (and the deviations therefrom) in the dual-phase Ti alloys and the homogeneity in their elastic properties. In addition, the results illustrate the different nature of elasticity relationships between the matrix and the secondary phase particles in the β + α and β+ ω alloys and explain the different mechanisms of elastic stiffening of the matrix by these particles. Single crystals of two different metastable (LCB and Ti15Mo) dual-phase β-titanium alloys with different phase compositions and different volume fractions of individual phases were investigated using resonant ultrasound spectroscopy (RUS) and transient grating spectroscopy (TGS). The combination of these two methods enables us also to discuss the homogeneity of the observed changes in the elastic constants by comparing the local data from TGS with the results from RUS representing the effective response of the whole crystal.

ABSTRACT. Low alloy bainitic steels are used for Reactor Pressure Vessels in nuclear power plants. Certification of these components requires strict compliance with minimum impact toughness values in the Ductile to Brittle Transition Temperature (DBTT) domain. As a result of the slow solidification of massive ingots, pressure vessel steels exhibit post-forging chemical segregation at a millimetric scale, and therefore local heterogeneities in composition and hardenability (upper vs lower bainite). In addition, the large wall thickness of such parts implies heterogeneous thermal histories during heat treatments, e.g. during water quenching. Lower bainite, with fine grains and/or small precipitates, is known to be tougher than coarser upper bainite. Moreover, recent work suggested that brittle fracture may initiate from molybdenum-rich carbides [1]. Until now, investigations, including [1] focused on lab-scale specimens.

The present study addressed the transposition of known laboratory results to the industrial reality by considering a full-scale part after monitored quenching. It focused on two regions with average cooling rates of 1000°C/h and 4000°C/h. These materials were slowly reheated and tempered at 645°C for 2h to 20h. The bainitic matrix and carbide size distributions were quantified in both segregated and non-segregated regions.

An increase/decrease of 30°C in the Charpy DBTT was observed after a 20h tempering compared to a 2h tempering. For each tempering condition, the nature of the brittle fracture initiation sites was investigated for specimens broken between -100°C and -20°C. Initiation sites were identified as inclusions, Mn/Mo-rich carbides, ductile ridges, and micrometric inter-granular areas. Mo-rich particles seemed to be present in most sites for particular tempering conditions. The effect of the cooling rate and tempering time on the nature of the initiation sites, in relation to the microstructure, is then discussed.

[1] P. Chekhonin, A. Das, F. Bergner, et E. Altstadt, Nuclear Materials and Energy 37 (2023). 101511

ABSTRACT. Laser-based resonant ultrasound spectroscopy (RUS) is an experimental technique where elastic properties of millimeter-sized samples are determined from their free vibrations. By using a laser vibrometer, resonant frequencies and modal shapes of vibrations are detected by scanning one side of the elastically vibrating sample. The precise determination of resonant spectra by the laser-based RUS technique allows measurements of the full set of elastic coefficients even for highly anisotropic materials, when several dozens of resonant modes are detected. The presented study focuses on polycrystalline pure alpha-titanium processed by equal channel angular pressing (ECAP). After four repetitions of the ECAP process, the grain size was reduced to sub-micrometer size with a strong (0001) texture, which was preserved even after annealing at various temperatures. Due to the hexagonal structure of pure Ti, the strong texture in the polycrystalline material results in its significant elastic anisotropy. This is evident in the distribution of Young’s modulus, as determined through RUS measurements, where the maxima of Young's modulus align with the direction of the (0001) texture maxima. Additionally, as the laser-based RUS is fully contactless, the ECAPed Ti samples were placed into the chamber with precise temperature control, where resonant spectra were detected along temperature cycles up to 590 °C. This allowed us to observe several internal processes affecting elastic moduli (related to the resonant frequencies) or internal friction (related to the width of the resonant peaks).

ABSTRACT. Irradiation Assisted Stress Corrosion Cracking (IASCC) affects the internal structures of Pressurized Water Reactors, leading to the intergranular failure of austenitic stainless steel components. After irradiation, slip discontinuity at grain boundaries has been shown to strongly correlate with intergranular cracking. This is due to the impingement of slip bands at grain boundaries, which leads to high local stresses that may be responsible for cracking. As the irradiation level increases, fewer slip bands are observed for a given strain level, resulting in higher local stresses. Therefore, it is crucial to obtain a reliable criterion that can predict slip discontinuity at grain boundaries in austenitic stainless steel as a function of both deformation and irradiation level for the modelling of IASCC. However, no such criteria are currently available in the literature. In this study, in-situ SEM tensile experiments on an unirradiated and two proton-irradiated 304L specimens were conducted sequentially through two increments of plastic strain (2.5% up to 5%). The zones of interest were mapped using Electron Back Scattered Diffraction before deformation, followed by Scanning Electron Microscope images of the same zones after each strain increment. Slip transfer is evaluated for all defined grain boundaries, based on their local crystallographic orientations and the analysis of slip traces. The activated slip system in each grain is assessed using the Schmid criterion, assuming either uniaxial stress conditions or using FFT simulations based on the real microstructure. The experimental data at the irradiated state are consistent with the criteria reported in the literature for FCC materials. Finally, we discuss the effects of irradiation and deformation.

ABSTRACT. Repairing damaged industrial parts poses a significant industrial challenge: cost reduction, increased lifetime and wastes avoidance are some of the pursued objectives. Applying conventional Additive Manufacturing repair processes, which feature transformation under liquid state, on structurally hardened aluminum-based alloys, is complicated by their metallurgical characteristics and the difficulty of subsequent heat treatment in the case of massive parts. This study focuses on Additive Friction Stir Deposition, with the aim of validating this repair route in the context of a reusable launch vehicle application. The behavior of the interface between the damaged part to be repaired and the material deposited on the surface will be particularly investigated. The methodology is the following. First, optical and scanning electronic microscopies are used to analyze the microstructure of repaired samples, particularly the local crystallography. Then an experimental study is conducted in order to characterize the mechanical behavior of the repaired parts. In-situ SEM tensile tests are performed, coupled with digital image correlation analysis based on lithography and speckle patterns to access the local microstructural strain fields. Various areas were explored, considering the microstructure variations in the repaired parts : the original material, the bulk deposited material and the interface between them. The impact of several microstructural features in plastic deformation localization is investigated. Coarsest intermetallic compounds are demonstrated to be fragile, cracking at high loads as well as triggering high strain concentration in their vicinity. Crystallography parameters and deformation fields were also correlated, with results dependent on the analyzed area's location. Grain boundaries are also identified as sites of high plastic strain. However, because of the interdependence of the contributions to plastic deformation of each feature type, they cannot be analyzed separately. Consequently, a scenario for explaining plastic deformation as a function of local microstructure is proposed, taking these interconnections into account.

ABSTRACT. Olivine is the most volumetric abundant mineral phase in the upper mantle and also the one which deforms the most and controls the rheology of the upper mantle. Deformation mechanisms in olivine have attracted considerable attention since several decades. One of the problems with this orthorhombic mineral is that there are not enough slip systems to produce a general deformation. The observation of a non-linear deformation regime depending on the grain size has led to the suggestion of the possibility of slip at the grain boundary [1], which has only recently been demonstrated microstructurally [2]. In this work we show that under high stresses, this grain boundary sliding can be due to the amorphization of the grain boundary and to the flow of this amorphous intergranular phase [3]. We show how nanomechanical testing in situ in the TEM allows to characterize this individual mechanism as well as the rheology of amorphous olivine. We finally propose that this mechanism of stress-induced amorphization is an important deformation mechanism in its own right under conditions of high stress [4].

[1] Hirth, G., & Kohlstedt, D. (1995) Experimental constraints on the dynamics of the partially molten upper mantle: 2. Deformation in the dislocation creep regime, J. Geophys. Res., 100, 15,441–449. [2] Bollinger, C., Marquardt, K. & Ferreira, F. (2019) Intragranular plasticity vs. grain boundary sliding (GBS) in forsterite: microstructural evidence at high pressures (3.5–5.0 GPa). American Mineralogist 104, 220–231. [3] V. Samae, P. Cordier, S. Demouchy, C. Bollinger, J. Gasc, S. Koizumi, A. Mussi, D. Schryvers & H. Idrissi. Stress-induced amorphization triggers deformation in the lithospheric mantle. Nature, 2021, 591, 82 [4] Idrissi, H., Carrez & P.Cordier, P. (2022) On amorphization as a deformation mechanism under high stresses. Current Opinion in Solid State & Materials Science. 26(1), 100976

ABSTRACT. Refractory compositionally complex alloys (RCCAs) may exhibit improved high-temperature resistance compared to face-centered-cubic (FCC) CCAs and superalloys. However, the brittleness of most CCAs at room temperature limits their applicability, while the role of the individual microstructural components has not yet been studied in detail. To understand the influence of microstructure on the deformation behaviors of these alloys, we conducted micro-mechanical experiments, including nanoindentation and micro-pillar compression tests, on a representative NbMoCrTiAl alloy at room temperature. The indentation at the grain boundaries showed increased shear stress and hardness compared to the matrix (ordered B2 crystal structure) due to the presence of intermetallic precipitates (C14 and A15 phases). Although the NbMoCrTiAl alloy exhibited no ductility at the millimeter scale in previous compression experiments, the micro-pillars containing a grain boundary with precipitates demonstrated higher yield strength and significant plastic strain >30% at room temperature. Numerous slip lines were observed inside grains, while cracks and sometime fracture occurred at higher levels of deformation. The grain boundaries containing precipitates appear more likely to exhibit crack initiation and propagation, while only in few cases catastrophic failure of the pillars was observed.

ABSTRACT. It has been widely accepted that in polycrystalline materials at high temperatures, low strain rates, and small grain sizes, grain boundary sliding dominates other deformation mechanisms. The grain boundary sliding often leads to stress concentration at grain boundary triple junction points which should be relieved to promote the sliding further. Because grain boundary sliding is a complex phenomenon which depends on material, grain boundary type, testing temperature, and likely, defects at the grain boundary, a quantitative understanding of grain boundary sliding is still missing. In this talk, we present temperature-dependent grain boundary sliding behavior in Ni bicrystal quantified by using in situ SEM micropillar compression. The orientation of crystals is close to <344> and <324> with a high angle grain boundary in between with a misorientation of ~ 20°. Micropillar compression tests performed on the pillars of diameter from 0.5 µm to 6 µm showed a mechanical size effect in both the crystals with a size exponent of ~ -0.5. Bicrystal micropillars are also tested which contain a 45° inclined grain boundary at the elevated temperature. In the talk, details on the experimental protocol as well as first insights into the size- and temperature-dependency of grain boundary sliding will be presented and discussed.

ABSTRACT. The viscoplastic response of metallic nano-crystalline films has been widely studied in the literature by means of nanomechanical testing, such as with in situ TEM experiments [1], [2] or dedicated on chip test methods [3]. The enhancement of ductility (as compared to large grain samples) has been attributed to different mechanisms, including grain boundary sliding, grain growth or kinematic hardening due to dislocation pile up [2], [4]. However, observations of the polycrystal deformation are challenging due to highly refined grain sizes. The correlative methodology developed in this work allows probing the relationships between the microstructural changes and the total strain field, at a scale never resolved before – i.e. sample size of 2.5 x 25 µm and strain field resolution of 50 nm. The aluminium films deposited by sputtering (210 nm thickness) are mechanically loaded with an on chip method [3] and then observed after deformation in the transmission electron microscope (TEM). Nanoscale digital image correlation (nano-DIC) reveals multiple necking regions appearing at low plastic strains and further spreading along the sample gauge without leading to critical failure. Automated crystal orientation mapping (ACOM TEM) indicates that strain localization bands correspond to grain boundaries (GB) and that the global texture remains unchanged. The local shear amplitude achieved by such GB sliding correlates, to some extent, with the GB character. The complementary results obtained by both techniques shed some new light on the link between GB mediated plasticity and enhanced macroscopic ductility.

REFERENCES [1] H. Idrissi et al., Applied Physics Letters, vol. 104, no. 10, p. 101903, 2014. [2] J. P. Liebig et al., Acta Materialia, vol. 215, p. 117079, 2021. [3] S. Gravier et al., J. Microelectromech. Syst., vol. 18, no. 3, pp. 555–569, 2009. [4] F. Mompiou et al., Acta Materialia, vol. 61, no. 1, pp. 205–216, 2013.

ABSTRACT. Dislocations in alloys with random solute distributions, short-range order, or clustering have a range of competing length and energy scales that establish overall energy barriers to dislocation motion. The flow stress then depends on many different underlying atomistic material parameters and emergent length scales. To gain understanding and to guide theory development, we show how a Peierls-Nabarro (PN) model can enable highly efficient scale bridging along with accurate parametric exploration of dislocation behavior as a function of (controllable) material parameters. First applications of the PN/ model to (i) understanding dislocation line tension in both fcc and bcc metals, (ii) the emergence of characteristic dislocation length scales in high entropy alloys (HEAs), and (iii) zero-temperature strength in HEAs, are then presented and discussed in the context of current theories.

ABSTRACT. The Portevin-Le Chatelier effect is a localization phenomenon resulting in the heterogeneity of the plastic deformation. Its accurate characterization is of primary interest for the sizing of industrial structures via finite element simulations. The present study seeks to ascertain the fidelity of our current models to describe correctly the heterogeneity of the PLC effect. Finite element simulations, utilizing the KEMC model [1], were used to simulate the PLC observed in our experiments.

In order to compare both simulations and experiments, tools were developed for the quantitative analysis of the PLC. Direct measurements of serrations amplitudes and periods enables the identification of trends in their dynamics. Subsequently, the use of tools derived from chaos theory, such as power spectrums and multifractal analysis, allows the quantification of the heterogeneity inherent in the Portevin-Le Chatelier signal. Our findings demonstrate that the simulations successfully re- produce the observed trends in our experiments. These outcomes not only provide insights into the potential application of these indicators in identification strategies but also offer avenues for refining pre-existing models.

References [1] N. Guillermin, J. Besson, A. K¨oster, et al.,“Experimental and numerical analysis of the Portevin–Le Chatelier effect in a nickel-base superalloy for turbine disks application,” International Journalof Solids and Structures, vol. 264, p. 112 076, 2023, issn: 0020-7683. doi: 10.1016/j.ijsolstr.2022.112076.1

ABSTRACT. The activation of prismatic slip in Mg and its alloys can improve the ductility. Experimental results demonstrate the softening effect of dilute addition of Zn and Al at/below room temperature and their strengthening effect at higher temperatures. This work aims at unraveling the mechanisms responsible for the effects of solutes on the ease of prismatic slip using atomistic simulations and theory. Based on first-principles Zn-solute/dislocation interaction energies, prism edge dislocation strengthening is investigated considering solute strengthening and dynamic strain aging via cross-core diffusion. Cross-core diffusion leads to a significant increase in the critical resolved shear stress for edge dislocation motion at high temperatures. But this stress is 60% below experiments. Turning to screw dislocations, we discuss mechanisms of solutes softening and strengthening, as revealed by first-principles results and a new neural network interatomic potential for Mg-Zn.

ABSTRACT. Plastic flow is conventionally treated as continuous in finite element (FE) codes, whether in isotropic or crystal plasticity. This approach, derived from continuum mechanics, contradicts the intermittent nature of plasticity at the elementary scale. During micropillar compression, the stress-strain curve exhibits strong serrations, linked to the abrupt activation of a very small number of slip planes. Acoustic emission on centimeter-sized single-crystal samples also demonstrate the non-chaotic but organized nature of plastic flow linked to dislocation avalanche interactions.

Understanding crystal plasticity at nanoscopic scale opens the door to new engineering applications, such as nanoscale machining and the design of radical new materials.

Various models in the literature also demonstrate the intermittence of plasticity, such as the mesoscopic tensorial model, molecular dynamics and discrete dislocation dynamics models. These models replicate the correlated nature of dislocation avalanches.

In this work, we propose a new approach to account for the intermittence of plastic deformation while remaining within the framework of continuum mechanics. We introduce a constant, the plastic deformation quantum, denoted as Δpmin, corresponding to the plastic deformation carried by the minimal dislocation avalanche within the material. The incremental model is based on the traditional predictor-corrector algorithm to calculate the elastoplastic behavior of a material subjected to any external deformation. The model is presented within the framework of small deformations for von Mises plasticity. The plastic strain increment Δp is calculated using normality rules and is accounted for only if it is higher than Δpmin. The simulations show that the introduction of the plastic quantum allows for the reproduction of the spatiotemporal intermittence of plastic flow, capturing the self-organization of plastic flow in complex loading scenarios within an FE model. Localized deformation bands spontaneously emerge in complex geometries, exhibiting correlation with stress drops observed in the tensile curves. The model is rate-independent.

ABSTRACT. Methods based on the Fast Fourier Transform are of high interest in micromechanics due to their computational efficiency in applications such as computational homogenization or Field Dislocation Mechanics (FDM). However, one of the main limitations of FFT calculations is the use of regular grids which prevents using different level of discretization in the domain, contrary to the Finite Element methods. To overcome this limitation, an adaptive FFT approach is proposed which allows to have finer grids in the area of interest and coarser grids elsewhere. The method relies on defining a map which deforms the structured grid, concentrating more discretization points in some target areas. Then, the differential operators involved in the governing partial differential equations are redefined based on the standard Fourier differentiation multiplied by the gradient of the mapping function. The result for a linear PDE is a system of equations that is solved using a Krylov solver.

This adaptive method is applied to the FDM problem, where strong gradients of the mechanical fields are found in very small areas around the dislocation lines. A finer grid was concentrated within the dislocation core in order to accurately represent the stress and strain resulting from a non-singular approach, while maintaining a coarser grid where the gradients were smaller. This method opens up the possibility of considering large Representative Volume Elements (RVE) of the microstructure maintaining an accurate description of the mechanical fields efficiently in terms of computational time and memory use.

The previous approach was used to study the elastic interaction of dislocations with other defects. The high accuracy of the mechanical fields computed around the dislocation allowed reliable calculations of the energy of the system which can be directly applied to Kinetic Monte Carlo models of defect evolution.

ABSTRACT. Bainitic steels have been studied for nearly a century. They are of high interest in the industry due to their unique combination of toughness and mechanical strength. Despite the current extensive knowledge on bainitic steels, many questions still remain. In particular, many observations and measurements suggest that local mechanical stresses are likely to play an important role on the final microstructure, which cannot be taken into account precisely within the classical mean-field models. An enhanced modelling approach, that takes into account the stress fields at the scale of the polycrystal, must therefore be implemented to gain understanding of the final microstructure. The present work focuses on the modeling of bainite formation at the scale of the initial austenite polycrystal using a cellular automaton coupled with an FFT-based elastic solver. The solver is optimized to efficiently handle 3D polycrystals with a significant number of prior austenite grains. The morphology of the bainite sheaves is simplified by considering ellipsoids adapted to plate/lath structures. The sheaves are assumed to grow along theoretical directions based on the phenomenological theory of martensite crystallography. Growth velocity in the main direction and carbon partitioning are calculated following a thermodynamical model. Furthermore, in a first step, the local stress field is considered only in the selection of the orientation of a new bainite sheaf. In a second step, it is also considered in the growth laws of bainite sheaves. The present work discusses the different sets of parameters that best predict the kinetics, microstructure and microtexture of bainite with respect to experimental characterization.

ABSTRACT. Metallic alloys used in nuclear power plants are under permanent irradiation which causes fast modification of their microstructure through a large variety of defects interacting with each other: interstitials, vacancies, point defect clusters, dislocations, grain boundaries (GBs), etc. In particular, segregation of atoms in these conditions can be observed at GBs, which can alter the structural integrity of the materials. Despite the numerous improvements achieved so far to understand radiation-induced segregation (RIS) at GBs through cutting-edge experimental or modelling tools, several observations remain unexplained. This might be due to the huge diversity of GB structures and the resulting difficulty to correctly describe their interactions with solute and point defect (PD) diffusion.

Recently, phase-field (PF) approaches have been developed to predict RIS behaviour in binary alloys for different conditions. However, in their formalism, the description of GB was still basic since the thermodynamic and elastic properties of the GB and the bulk phase were supposed to be the same, the GB being treated as a simple absorbing plane for PDs (“planar sink” model). As a consequence, these approaches fail to predict thermal segregation, which may interplay with RIS resulting in complex segregation profile at GBs.

To overcome the limitations of this “planar sink” model, we first propose in this work to better describe the thermodynamic heterogeneities between the bulk phase and the GB. For this purpose, a density-based model recently proposed in the literature is adopted, allowing to recover the well documented “W-shape” segregation profile observed experimentally under irradiation. Secondly, the elastic relaxation at the GB is modelled by different approaches, among which the Read and Shockley one for low angle tilt GBs, inducing complex segregation behaviours analysed in detail. Case studies will be presented on Fe Cr and nickel base model alloys for nuclear applications.

ABSTRACT. In shape memory alloys, the competition between interfacial and elastic strain energy contributions leads to the phenomenon of twin branching, i.e. to the refinement of the twin laminates close to the macroscopic interface between twinned martensite and austenite. Recently, within a discrete setting, Seiner et al. (2020) developed an explicit, low-energy construction of the branched microstructure that is able to realistically predict the twin spacing and the number of branching generations. In this work, we propose a 1D continuum model of twin branching. The free energy of the branched twin microstructure is introduced which comprises two contributions that correspond to the interfacial energy and to the elastic strain energy associated with branching. The elastic strain contribution is calibrated using the respective upper-bound estimate derived by Seiner et al. (2020). The total free energy is then minimized, and the corresponding Euler-Lagrange equation is solved numerically using the finite element method. The results of our model show a good agreement with the model of Seiner et al. (2020) in a wide range of physically relevant parameters. Additionally, energy dissipation effects can be included in our continuum framework. Both rate-dependent and rate-independent dissipation is considered and its impact on the evolution of the branched microstructure is studied.

ABSTRACT. We derive a semi-analytical model of intergranular normal stresses for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the local grain-boundary-normal stress and the corresponding uncertainties, as a function of the grain-boundary type, its inclination with respect to the direction of external loading and material-elasticity parameters. The knowledge of intergranular normal stresses is a necessary prerequisite in any local damage modeling approach, for example, to predict the initiation of intergranular stress-corrosion cracking, grain-boundary sliding or fatigue-crack-initiation sites in structural materials.

The model is derived in a perturbative manner, starting with the exact solution of a simple setup and later successively refining it to account for higher order complexities of realistic polycrystalline materials. In the simplest scenario, a bicrystal model is embedded in an isotropic elastic medium and solved for uniaxial loading conditions, assuming 1D Reuss and Voigt approximations on different length scales. In the final iteration, the grain boundary becomes a part of a 3D structure consisting of five 1D chains with arbitrary number of grains and surrounded by an anisotropic elastic medium. Constitutive equations can be solved for arbitrary uniform loading, for any grain-boundary type and choice of elastic polycrystalline material. At each iteration, the algebraic expressions for the local grain-boundary-normal stress, along with the corresponding statistical distributions, are derived and their accuracy systematically verified and validated against the finite element simulation results of different Voronoi microstructures.

ABSTRACT. This presentation focuses on simple yield-stress fluids, which are non-thixotropic viscoplastic soft materials exhibiting solid-like behavior at low stress levels and transitioning to non-Newtonian fluid-like flow above a critical stress. The most basic model to describe these materials is arguably the Bingham model [1], which assumes rigid behavior below a constant yield stress and Newtonian fluid behavior above it. More complex models include the Herschel-Bulkley [2] and Casson models [3], which account for non-Newtonian flow behavior beyond the yield stress.

Criticism has been raised regarding the assumption of a true yield stress below which only elastic deformation occurs [4]. This criticism arises from the observation of a limiting zero-shear viscosity plateau in typical yield-stress fluid systems like Carbopol microgels at various concentrations [5].

The nonlinear viscoelastic response of simple yield-stress fluids has received less attention but is the central focus of this presentation. By analyzing creep curves measured at different stress levels for Carbopol microgels, we will illustrate the validity of time-stress superposition for this system. This, in turn, allows us to formulate a comprehensive 3D nonlinear viscoelastic constitutive equation capable of describing nonlinear viscoelastic behavior, including creep and the transition to Herschel-Bulkley-like yielding, without the need for a conventional "yield stress."

References: 1. Bird, R. B., Dai, G. C. & Yarusso, B. J. The Rheology and Flow of Viscoplastic Materials. Rev. Chem. Eng. 1, 1–70 (1983). 2. Herschel, W. H. & Bulkley, R. Konsistenzmessungen von Gummi-Benzollösungen. Colloid Polym. Sci. 39, 291 (1926). 3. Casson, N. Rheology of disperse systems proceedings of a Conference. in Rheology of disperse systems (ed. Mill, C. C.) 84–104 (Pergamon Press, 1959). 4. Barnes, H. A. & Walters, K. The yield stress myth? Rheol. Acta 24, 323–326 (1985). 5. Roberts, G. P. & Barnes, H. A. New measurements of the flow-curves for Carbopol dispersions without slip artefacts. Rheol. Acta 40, 499–503 (2001).

ABSTRACT. Fracture in glassy polymers involves the rearrangement of atoms or the breakdown of covalent bonds, which cannot be accessed by experiments. At atomistic scales, molecular dynamics (MD) simulations are appropriate tools to reveal the physical mechanisms of fracture behavior. Various studies have been conducted on the fracture of polymers using MD simulations. However, most of them consider MD systems with uniform deformations at the boundaries, resulting in a limited size for the process zone during fracture. Due to the limitation of the total system size constrained by prohibitive computational costs, these studies neglect the effects of non-uniform deformations, which are, however, crucial in determining the fracture behavior of glassy polymers.

To overcome this, we consider an atomistic-to-continuum coupled system with an MD domain with non-periodic boundary conditions surrounded by a continuum domain solved by the Finite Element method. The continuum domain interacts with the MD domain in their overlapping region to provide appropriate boundary deformation conditions. The coupling is implemented through energy blending and the constraint of deformation consistency in the overlapping region. The constitutive model in the continuum domain is predefined to reproduce the bulk behavior in MD simulations. With this coupling method, we conducted fracture simulations for a sample of coarse-grained polystyrene with pre-cracks and aimed to extract the relation between the microscopic structure and the macroscopic behavior.

ABSTRACT. The macroscopic behaviors of materials are determined by phenomena that occur at different lengths and time scales. We show in this presentation that describing, predicting and understanding these behaviors may require models that rely on insights from electronic and atomic scales. Depending on the application, classical simplified approximations at those scales are insufficient, and quantum-based modeling is inevitable. This presentation explores how quantum effects can modify mechanical properties of certain molecular systems, from one-dimensional carbon structure to Ultra High Molecular Weight Polyethylene (UHMWE). Our study employs a high-fidelity modeling framework that combines two computationally efficient models rooted in first principles of quantum mechanics: Density Functional Tight Binding (DFTB) and many-body dispersion (MBD). DFTB is a semi-empirical method rooted in Density Functional Theory (DFT), and the MBD model is applied to accurately describe van der Waals dispersion interactions. Through various benchmark applications, we demonstrate the capabilities of this framework and the limitations of simplified modeling, like classical force fields. This framework serves as a practical tool that we hope will support the development of future research in effective ab-initio large-scale and multi-scale modeling.

[1] A. Tkatchenko, R. A. DiStasio, R. Car, and M. Scheffler. Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett., 108:236402, Jun 2012. [2] P. Hauseux, T.-T. Nguyen, A. Ambrosetti, K. Saleme Ruiz, S.P.A. Bordas, and A. Tkatchenko. From quantum to continuum mechanics in the delamination of atomically-thin layers from substrates. Nature Communications, 11(1):1651, 2020.

ABSTRACT. The study of carbon fibre composite (CFRP) laminates at high strain rates is one of the main challenges in the aeronautical industry. Several researchers have studied the effect of strain rate on CFRP laminates with a woven structure. Dynamic compression tests are mainly performed using the Hopkinson bar system (SHPB). The research community has not yet agreed on a robust methodology that accurately describes the formulation representing the high strain rate response of woven CFRP laminates. Over the past decades, several researchers have studied the effect of holes in CFRP to describe the effect of the stress concentration factor. Although many studies have developed numerical simulations to analyse the fracture process in CFRP based on fracture mechanics theories, there is little information on the strain rate dependence of woven fabric CFRP laminates with holes. In this work, a constitutive model is proposed to describe the mechanical behaviour of woven CFRP laminates including the strain rate dependence on the compressive properties. Finally, a FE modelling has been carried out using Abaqus/Explicit software of compression tests on CFRP laminate specimens with holes, at different strain rates (Quasi-Static and dynamic) using different fibre orientations. The results of the simulations have been validated based on the results of an experimental campaign.

ABSTRACT. As their name suggests, 3D-fabric reinforced composites, are manufactured by intertangling yarns together in three-dimensional space to create a near-net-shape dry fabric preform. After infusing this preform with a resin matrix system, a light-weight component is created which demonstrates both high in- and out-of-plane stiffness and strength. The through-thickness reinforcements present in this material class, prevent delamination and allow for stable and progressive damage growth in a quasi-ductile manner.

Composites with 3D-fabric reinforcement present several advantages, both in terms of their manufacturing and mechanical performance. However, the woven yarn structure creates a material with a number of interesting behaviours and features which need to be accounted for when developing a model to predict how the material will deform and eventually fail. To begin with, these materials are highly anisotropic and show varying levels of non-linearity depending on loading mode. This non-linearity can be due to a variety of subscale behaviours: microcracking in the matrix or fibre-bundles, yarns straightening and fibres breaking and viscous effects from the polymer matrix.

One of the big questions when working with this class of materials is then; what is causing the non-linear behaviours and how can they be modelled in a physically meaningful way. For this reason, a testing campaign initially proposed by Zscheyge et al. (2020) for laminated composites is carried out in this work. It involves cyclically loading and unloading test samples at different orientations with creep and relaxation period in between. From a single test, it is then possible to determine how permanent strains, stiffness degradation and rate dependence develop as the deformation increases. A phenomenologically based macroscale model is then developed and presented. It considers the material as a homogenous and anisotropic solid. The experimental tests results are used to formulate and calibrate an anisotropic viscoplastic-damage model for 3D-fabric reinforced composites

ABSTRACT. Metal-ceramic composites represent advanced materials that combine the hardness of ceramics with the strength and toughness of metals, resulting in high stiffness, wear resistance, and thermal properties. They find applications as structural materials in the aerospace, automotive, and energy sectors, where they are often subjected to severe quasi-static and dynamic loads. Employing phase-field modeling to homogenized domains characterized by effective mechanical properties serves as a solution to avoid the computational costs and limitations associated with modeling real microstructures in metal-ceramic composites. However, determining the appropriate length scale parameter is crucial for successful implementation.

Following [1], this study aims to propose an experimental approach for establishing a physically meaningful length scale parameter in the phase-field modeling of quasi-static and dynamic fracture in metal-ceramic composites with brittle or ductile matrices. To accomplish this objective, a series of quasi-static and dynamic fracture tests are performed at room temperature using a 50J instrumented impact pendulum. The tests involve three-point bending on mode I and mixed-mode I/II V-notched specimens made of Al2O3/Cr and Al2O3/AlSi12 composites. The Al2O3/Cr samples exhibit brittle fracture behavior, while the Al2O3/AlSi12 samples show ductile fracture behavior. Detailed studies of the fracture surfaces are conducted to identify fracture micromechanisms in the investigated composites and measure the length of the fracture process zone or the stretching zone ahead of the initial crack tip. The length scale parameter in the phase-field modeling is then set equal to the measured length.

The fracture toughness is determined from the phase-field simulations by fitting the numerical load-displacement curves to the experimental data. The numerically and experimentally determined fracture toughness values are compared to validate the proposed method for the experimental determination of the phase-field length scale parameter.

[1] Darban H., Bochenek K., Węglewski W., Basista M., Metallurgical And Materials Transactions A, Vol. 53, p. 2300–2322, 2022.

ABSTRACT. The effect of initial defects on the compression and buckling behaviour of thermoplastic composites stiffened panels is assessed via an experimental and numerical approach. In the aerospace industry, there is a constant need for increasing the production rates. The manufacturing process of composite entails defects that could impact the mechanical behaviour. The exemption for the acceptability for defects becomes a major industrial issue. Whilst a certain wealth of knowledge is available, the effect of defects on the compressive behaviour of composites structures requires further study. Two composites panels featuring Z-shaped stiffeners are manufactured using a carbon fibre reinforced thermoplastic matrix. Ultrasonic scans and X-ray computed tomography are used to characterize defects. During the compressions tests, the displacement fields are monitored using optical cameras and the damage evolution using thermography and acoustic emission sensors. Numerical simulations are performed using two approaches: one based on the use of shell element, while the other incorporates a combination of shell and continuous elements. The strategies proposed for representing defects involve explicitly meshing delamination and penalizing the material elastic properties at the locations in which voids are detected. With respect to the first panel, the second panel exhibits higher levels of porosity at its skin and lower levels of initial delamination at the stringer’s webs. The buckling modes are detected using the out-of-plane displacement fields. Surprisingly, the panel featuring less defects collapsed at a lower load. Since the panels are free to rotate around the loading axis at the bottom clamp, the dissymmetry given by both the panel geometry and the defects induced an additional torsional deformation leading to an angle of twist. The angle of twist and the buckling mode are properly captured by the numerical simulations. The effects of defects are discussed based on both the experimental tests and the numerical simulations.

ABSTRACT. Conventional manufacturing methods for lightweight composites are highly energy consuming. For example, oven curing has been estimated to consume approximately 20 MJ/kg largely due to excess heating of chamber volumes and molds. Electromagnetic induction heating on the other hand is a highly-promising alternative manufacturing method with low power consumption, high heating rates and flexibility to deliver contactless energy directly to the targeted location of the produced part. A prerequisite for this method are favorable electromagnetic properties of constituents that enable heat generation under the presence of electromagnetic field. Due to physical properties of carbon fibers, carbon/epoxy composites are suitable for induction heating. However, the heating mechanisms under induction heating are notably different from those in conventional oven curing - the fibers and their contact points act as heat sources and hence it is meaningful to study the development of fiber/matrix bonding strength and residual stresses in induction-cured composites. In the present study a series of micro-mechanical studies was performed experimentally and numerically. An induction heating rig consisting of a moving coil, thermal imaging camera and data processing unit, capable of ensuring a sufficiently uniform heat distribution during curing of highly anisotropic composites was developed and applied for manufacturing of unidirectional and cross-ply material samples. From unidirectional materials, longitudinal and transverse strength was determined, while micro-crack evolution and residual stresses were obtained from cross-ply material tests. Optical and scanning electron microscopy was used for quantification of micro-damage and for qualitative inspection of fracture surfaces. For reference the degree of cure was measured using DSC analysis. Obtained properties were compared with reference material obtained using conventional oven curing. Numerically, simulations of residual stress development during induction curing were performed using commercial FEM software using Schapery-based time-dependent material models. Boundary conditions corresponding to internal heat generation in carbon fibers were applied.

ABSTRACT. Lightweighting of components in transport systems by the substitution of traditional bulk parts by architected structures has been lately facilitated by the advent of metal additive manufacturing methods. Numerous studies in the literature have reported the relationship between the architecture, the material microstructure, and the mechanical behavior of lattice structures. However, these studies have mostly been conducted at room temperature, and the high temperature behavior of architected materials remains largely underexplored.

In a recent study the current authors reported for the first time the occurrence of serrated flow at moderate temperatures in strut-based Inconel 718 lattices produced by laser powder bed fusion (LPBF) [1]. It was shown that the testing conditions (temperature, strain rate) under which serrated flow appears are topology-dependent. The origin of such dependence is unknown. Moreover, the fundamentals of serrated flow in bulk samples of Ni-based superalloys have still not been well established. While in steels and Al alloys flow instabilities have been linked to the occurrence of dynamic strain aging (DSA), the origin of serrated flow in Ni-based superalloys remains elusive.

In this work we investigate the occurrence of serrated flow in Inconel 718 strut-based lattices with different geometries manufactured by LPBF. Flow instabilities are investigated at temperatures ranging from 300 to 600°C. It will be shown how the combination of experiments and finite elements modeling (FEM) sheds new light on the origin of the critical strain at which the first serrations appear.

[1] S. Banait, M. Campos, M.T. Pérez-Prado, Mat. Lett. 353 (2023) 135314.

ABSTRACT. Selective Laser Melting (SLM) of metallic biomaterials, an additive manufacturing (AM) technique, offers rapid fabrication with improved bulk properties. This study investigates the impact of heat treatment on residual stress, bulk properties, and tribological performance of SLM 316L stainless steel (316L SS) components. Experimental analyses, including X-ray diffraction and microscopy, characterize residual stress and microstructural changes induced by varying heat treatment parameters (e.g., 650 °C and 950 °C). Micro-hardness measurements and tribological tests are also conducted to evaluate the mechanical and tribological behavior for both as-printed and heat-treated specimens. Surface integrity, such as surface roughness, morphology, and microstructure, reveals significant improvements at 650 °C and 950 °C compared to as-printed samples. A micro-hardness values range from 270 ± 4 to 357 ± 7 HV0.1, with a slight decay at 650 °C. Further, the tribological analysis shows similar behavior for as-printed and 650 °C specimens (COF: 0.34 and 0.33, respectively), with a slight improvement at 950 °C (COF: 0.29). The volumetric wear loss values were also calculated, and the outcomes aligned with the friction performance. Furthermore, the correlation between experimental and simulation results, using SIMUFACT Additive software, explores the residual stress distribution on all faces. The residual stress values for as-printed, 650 °C, and 950 °C specimens range from 354 MPa (compressive) to 722 MPa (tensile), 308 MPa (compressive) to 207 MPa (tensile), and 328 MPa (compressive) to 196 MPa (tensile), respectively. The results indicated that the as-printed part exhibits maximum tensile residual stress, decreasing with heat treatment strategies. The obtained residual stress values from the simulation results are also compared with the XRD data, and it found that maximum residual stress values are in line with simulation results, emphasizing the research's contribution to correlating experimental and simulation results for additively manufactured metallic components with tailored heat treatment strategies.

ABSTRACT. Relatively fast numerical strategies have been developed for the simulation of temperature kinetics [1] and stresses [2] arising in directed energy deposition (DED). Operando synchrotron X-ray diffraction measurements during additive manufacturing of a 316L stainless steel thin-wall have recently been used to validate numerical predictions of residual elastic strain distribution taking place after complete cooling [3]. However, X-ray diffraction provides only the lattice strain coupling both thermal expansion and elastic strain, and it is demonstrated that the classic direct estimation of temperatures and cooling rates neglecting elastic strain leads to significant errors under DED conditions, which can be corrected by using numerical simulations.

To do so, the model[1] should be further validated so that it can be safely used to decouple thermal and elastic contributions in X-ray diffraction measurements. Indeed, despite the fact that infrared measurements have been used to validate simulations at the scale of the entire part, some local assumptions were necessary in [1] to reach short computation time, and the transient temperature distribution in the melt pool vicinity may be subjected to errors, and has not yet been properly validated against experiments. In this contribution, the transient thermal+elastic strain taking place during fabrication is derived from X-ray diffraction measurements. The resolution of acquired images is sufficient to observe strain distribution in the melt pool vicinity, but not sufficient to clearly identify the melt pool shape though. Good agreement is observed with the numerical counter-part, which thus demonstrate the ability of the fast numerical approach [1] to provide reliable results in the melt pool vicinity, and to be used to decouple thermal and elastic contributions in X-ray diffraction measurements as suggested in [3]. [1] Weisz-Patrault,D.(2020). Additive Manufacturing, 31, 100990. [2] Weisz-Patrault,D., Margerit,P., Constantinescu,A.(2022). Additive Manufacturing, 56, 102903. [3] Gaudez,S., Weisz-Patrault,D., Abdesselam,K.A., Gharbi,H., Honkimäki,V., van Petegem,S., Upadhyay,M.V.(2023)Preprint. Additive Manufacturing

ABSTRACT. In recent years, additive manufacturing (AM) has shown immense potential towards applications in the field of automotive, aerospace, biomedical, energy, etc., owing to its efficient material usage and ability to rapidly prototype metallic parts of any shape. However, the action of extreme thermal loads generates significant residual stresses that impact the mechanical response and failure of these parts.

This study proposes an experiment-driven modelling and simulation approach to understand the origin and formation of intergranular residual stresses and localization of plastic strain during post-process laser scanning of an AMed stainless steel.

Using a novel coupling between a continuous-wave laser and a scanning electron microscope, a series of single-scan laser scanning experiments were performed on AM 316L stainless steel microstructures. Detailed analysis revealed refinement of cellular microstructure, formation of misorientation bands, and hence, geometrically necessary dislocations (GNDs) within the lasered zone.

This information was used to guide the development of a polycrystalline thermo-elasto-viscoplastic finite element (TEVP-FE) model in small-strain framework to understand the evolution of intergranular stresses and plastic strains. The model predicted polar dislocation density distribution was compared with the experimentally measured one. The role of laser scanning induced microstructure refinement, elastic anisotropy and plastic heterogeneity on the formation of local residual stresses and plastic strains was then analysed. These results will be presented in this talk.

ABSTRACT. Microtruss-based architectured materials offers an unprecedented range of mechanical properties, expanding their potential applications. Their remarkable stiffness-to-weight ratio has attracted significant attention in transportation research. However, in most cases, the proposed architectures are anisotropic on a large scale, making it difficult to characterize their response to fracture, in particular [1]. In our work, we designed a new class of microtruss-based metamaterials, characterized by isotropy at small scales. This led us to develop a new set of numerical tools to create such structures and their digital twins to predict each of their mechanical properties [2]. We will see that these novel microtruss-based materials of locally isotropic structures can reach an unprecedented stiffness-to-density ratio, closely approaching the theoretical upper bounds established by Hashin-Shtrikman for isotropic porous solids [3]. Conversely, they exhibit rather weak compression strength and we will discuss an on-going AI-based approach to increase this strength by introducing a complex spatial modulation of the local microbeam features (diameter, shape, constituent material…) in an appropriate manner.

References: [1] Shaikeea, A. J. D., Cui, H., O’Masta, M., Zheng, X. R., & Deshpande, V. S. (2022). The toughness of mechanical metamaterials. Nature materials, 21(3), 297-304. [2] A. Montiel, T. Nguyen, C. L. Rountree, V. Geertsen, P. Guenoun, and D. Bonamy Effect of architecture disorder on the elastic response of two-dimensional lattice materials (2022), Phys. Rev. E 106, 015004 [3] Z. Hashin, Shtrikman A variational approach to the theory of the elastic behaviour of multiphasematerials, S. J Mech Phys Solid (1963) 127e140.

ABSTRACT. Porous materials with heterogeneous pore features are used in many branches of technology, from lightweight structures to biomedical implants and electrodes. These materials derive their properties from their internal architecture, which is often poorly controlled via conventional manufacturing routes (e.g. foaming, templating). Here, we combine laser powder bed fusion (LPBF) additive manufacturing technology with computer design to fabricate metallic cellular architectures with heterogeneous, yet precisely-controlled, pore features. The materials of this study contain through-thickness pores - of micrometric circular size - randomly dispersed into a dense metallic matrix. Their porous architecture is generated numerically using a random sequential absorption algorithm [1, 2], and is 3D-printed out of AlSi10Mg powders. In this work, we focus specifically on elucidating the impact of a wide set of LPBF parameters on the topological features of random architected materials with through-thickness voids. In addition to the analysis of the pore topological imperfections, our work also examines the role of the metallurgical defects inside the matrix. These too are greatly impacted by the LPBF parameters. To assess their influence on the mechanical response of the cellular materials, modelling tools were developed to incorporate those defects in finite element models of the porous structures. The results of simulations were found to be in good agreement with the results of compression experiments. Collectively they showed that the mechanical response of metallic cellular materials is less sensitive to topological imperfections, whereas metallurgical defects within the matrix are the main precursor of damage.

[1] M.G. Tarantino, O. Zerhouni, K. Danas, Random 3D-printed isotropic composites with high volume fraction of pore-like polydisperse inclusions and near-optimal elastic stiffness, Acta Materialia 175 (2019) 331–340. [2] Z. Hooshmand-Ahoor, M.G. Tarantino, K. Danas, Mechanically-grown morphogenesis of Voronoi-type materials: Computer design, 3D-printing and experiments, Mechanical of Materials 173 (2019) 104432.

ABSTRACT. Irreversible responses in materials encode information about past driving; however, this information is often challenging to recover. In this study, we introduce a beam counter metamaterial designed to track applied driving cycles by elastically deforming into easily interpretable internal states. We further demonstrate how combining multiple of these counters together allows us to extract rich information from applied driving, considering both the magnitude and order of driving events. Finally, we realize a 'lock and key' metamaterial with a unique internal state reachable only through the application of a specific 'key' driving input. This design strategy is robust and scalable, laying the foundation for the development of 'memory materials' that maximize the recoverable information stored about past driving.

ABSTRACT. Nanoporous metal structures are of high interest in both academic research and industry due to their tunable mechanical properties and light weight. However, understanding the mechanical properties of these materials is still a challenge. Existing research has demonstrated that among many other parameters (relative density, ligament diameter, specific surface area, etc.), topology plays a key role in determining the structural properties. Despite the nearly countless ways to define the topology of a porous structure, current works have focused mostly on random Al or Au structures and on several common topologies such as FCC, BCC, gyroid, and others. This study focuses on an alternative set of topologies reported in the context of the reticular chemistry of nanoporous (non-metallic) crystalline materials. Specifically, by performing a series of Molecular Dynamics (MD) simulations, we examined 22 topologies in terms of yield stress and Young's modulus, while comparing them to stochastic nanoporous aluminum structures. The results show that structures constructed with predefined topologies have superior Young's modulus and yield strength. Moreover, distinct scaling laws of mechanical properties are observed for different topologies, revealing the relationship between topology and mechanical behavior in nanoporous materials. Additionally, Machine learning models were implemented to connect numerical descriptors of studied structures with their mechanical properties.

ABSTRACT. The field of additive manufacturing (AM) has evolved significantly over the past decades, notably through systematic numerical modeling efforts, with the aim of manufacturing complex structural parts with good control precision, virtually unlimited design freedom, improved and even locally variable properties. Numerical modelling has become a decision-making tool for revealing the complex process-structure-property-performance relationships in cold spray (CS) process. It is used to speed up the development and qualification of CS coating, CSAM and CS repair techniques. The objective of this work is to investigate high-fidelity modelling and simulation of multiple physical phenomena (fluid dynamics, heat transfer, particle dynamics, non-equilibrium transformations and material behavior) involved in CSAM process. A good understanding of these phenomena is a key factor for predicting the optimal process parameters, the suitable microstructure and improving mechanical properties under different impact conditions. The adopted strategy consists in integrated Multiphysics, multiscale computational model (IMMCM) with four main ingredients: 1. Computational fluid dynamics (CFD) simulation for a high-pressure nozzle with axial powder injection including supersonic gas flow, particle acceleration, particle trajectory and heat transfer 2. Meso-scale finite element method (FEM) and atomic-scale molecular dynamics simulation for single particle impact behavior and interfacial bonding characteristics 3. Meso-scale FEM simulation of multi particle-substrate impact behavior and part build-up using coupled eulerian-lagrangian technique to predict surface morphology and porosity 4. A quantitative understanding of the microstructural evolution, damage initiation of cold sprayed deposit materials using physically dislocation density-based computational microstructural modelling, combining experimental investigations and validation efforts, taking into account topological effects on phase distribution for CSAM optimization. The developed model is combined with experimental investigations to contribute to a good understanding of the mechanisms that take place during the process. The obtained results pave the way to establishing a correlation between the process parameters and the state of the material

ABSTRACT. Sintering is the key stage of additive manufacturing of micro-scale metal components. For the case of free form (statically determinate) structures, the existing sintering theories predicts no long-range mass transport or distortion for uniformly heated particles. However, in sintering-based advanced additive manufacturing processes, permanent part distortion is observed [1]. Sintered needles and walls first develop large transient curvature and then smaller permanent curvature, features not predicted by standard sintering models. We conclusively demonstrate that part distortion during sintering is a result of a long-range mass transport. Two possible mass transport mechanisms are defined and the macro-scale continuum model applicable to both formulated. The macro-scale model accurately predicts the transient and permanent distortion observed during our experiments, including their size dependence, irrespective of the actual mass transport mechanism.

To distinguish between the possible mass transport mechanisms, the meso-scale computational model is formulated based on the phase filed framework and encompassing: diffusion through the grains and interfaces, particle motion and elasticity of the grains. The meso-scale model represents significant mathematical challenges, since it connects two heterologous continua: lattice continuum for the solids with diffusion [2], and mass continuum for the gas, which flows out in the initial phases of sintering and is trapped and compressed in the later stages. Preliminary meso-scale computational results are presented.

References [1] Ritchie, S., Kovacevic, S., Deshmukh, P., Mesarovic, S.Dj., Panat, R. 2023 Shape distortion in sintering results from nonhomogeneous temperature activating a long-range mass transport. Nature Communications 14, 2667. https://doi.org/10.1038/s41467-023-38142-z [2] Mesarovic, S.Dj. 2016 Lattice continuum and diffusional creep. Proc. R. Soc. A 472, 20160039. http://dx.doi.org/10.1098/rspa.2016.0039

ABSTRACT. Wire arc additive manufacturing (WAAM) is a widely studied technology known for its high deposition rate and capacity to fabricate large components. Despite the advantages of additively manufacturing aluminium alloy components, challenges such as porosity, surface oxidation, cracking, warping, residual stresses, and geometric accuracy limit its widespread application. Among these challenges, porosity is considered a factor that will affect the mechanical properties of WAAM-manufactured aluminium alloys. Numerous strategies to address these challenges have been explored in scientific literature, focusing on optimizing parameters such as heat input, wire feed rate, metal transfer mode, wire batch, shielding gas flow, and shielding gas preheating. While these techniques show potential improvements in mechanical properties, further development is still needed. This study investigates the potential of automatic interlayer Laser Cleaning (LC) in the WAAM process. LC is an environmentally friendly method that is commonly used to remove rust, paint, oxide, and other contaminants from metal surfaces. The benefits of LC have been successfully demonstrated for conventional joining applications using arc and laser beam welding since 2014. Its application in WAAM of aluminium alloys has not yet been explored. To assess the benefits of LC in WAAM production of aluminium alloys, parts were produced using ER 5183 and ER 2219 aluminium alloys with and without laser cleaning between deposited layers. The removal of the oxide layer is expected to reduce the percentage, size, and distribution of porosities, directly influencing mechanical properties. The samples underwent characterization using computed tomography, tensile testing, and SEM/EDX analysis to provide a comprehensive comparison and evaluation of the impact of laser cleaning on WAAM-produced aluminium alloys. The study aims to numerically quantify the influence of interlayer laser cleaning on the mechanical properties of WAAM-manufactured aluminium alloy components.

ABSTRACT. The goal of this study is to provide new alloy solutions for the MELD manufacturing technology, a solid-state additive manufacturing technique, based on the additive friction stir deposition. Post deposition treatements are usually necessary to enhance mechanical properties of the printed parts. In order to take into account environmental issues, the aim of this presentation is to present an example of application that does not require post-process thermal treatments. Al-Mg alloys, hardened by magnesium in solid solution, were the ideal candidate. This type of alloy, mainly used in the construction of boat hulls, is known to form Al3Mg2 precipitates at grain boundaries. The susceptibility to stress corrosion cracking as result of alloy ageing, known as “sensitization” is the consequence of this precipitation in such a corrosive environment. To overcome this issue, the addition of Al3(Sc,Zr) core-shell dispersoids, potential heterogeneous nucleation sites for Mg, was studied. Thanks to isothermal artificial ageing treatments punctuated by measurements of thermoelectric power, it was shown that the presence of Al3(ScZr) dispersoids in the alloy accelerated Mg precipitation. Atom probe tomography analyses subsequently confirmed the segregation of Mg on the surface of these dispersoids.

This presentation will focus on the influence of the MELD process on (i) the alloy microstructure, (ii) Mg precipitation and (iii) Al3(ScZr) dispersoids stability.

After MELD, the microstructure appears finer, equiaxed and homogeneous. EBSD analyses shows a grain size for binary AlMg alloy independent of the tool rotation rate. However, the grain size of AlMgScZr alloys increases with rotation rate, questioning the stability of dispersoids under shear. Dispersoids have been studied with TEM and APT before and after the MELD process. Mg precipitation kinetics and corrosion sensitivity were finally characterised to outline the influence of the MELD on sensitization.

ABSTRACT. When a liquid droplet comes near a hot surface, vaporization can become sufficient to cause the drop to levitate—this is the Leidenfrost effect. Vaporizable soft solids, e.g., hydrogels, can also exhibit levitation or, additionally, a sustained bouncing effect. In the floating liquid case, vapor pressure and surface tension balance create an inversion of curvature on the droplet underbelly.  Naively, one might expect that in the case of a floating soft solid, vapor pressure and elasticity would create a similar equilibrium with a similar curvature inversion, and indeed theoretical work predicts this is the case.  We use high-speed interferometric imaging to measure the 2D height profile underneath a floating hydrogel sphere, and to our surprise, we find that there is no curvature inversion.  Instead, a downward-facing conical shape is created underneath the sphere.  We speculate that the interplay between vaporization rate, gas flow rate, and shape is essential for this behavior.

ABSTRACT. Many problems involve an interplay between granular matter and elastic structures, including food packaging (e.g. coffee beads in plastic bags), cell membrane deformations in plants, or soil-root interactions. Here, we explore this coupling in a simplified system, investigating how an elastic structure deforms under the weight of grains. We set up a two-dimensional experiment consisting of an extensible ribbon, placed between two walls, onto which grains are deposited to form a heap. We show that the ribbon, as it deforms, acts as a reservoir of grains, altering the shape of the grain pile, including the angle of repose and the spreading of the heap, depending on the initial tension and rigidity of the ribbon. By increasing then significantly the volume of grains, the ribbon elongation and the spreading of the heap eventually saturate above a threshold related to the nonlinear behavior of the ribbon.

ABSTRACT. Liquid crystal elastomers (LCEs) represent a class of responsive materials capable of substantial and reversible deformations when subjected to external stimuli, such as light. These materials hold promise for advancing propulsion systems, particularly in emulating cilia-like motions. Hence, understanding the fundamental physics governing their dynamic response within a fluid medium under light exposure is crucial for optimizing their shape and augmenting their performance. In this study, we've developed a multi-physics fluid-structure interaction model in COMSOL software to explore the self-oscillation phenomenon of an LCE beam immersed in a fluid and subjected to illumination. The beam is clamped at one end and exposed locally to constant-intensity light near the fixed edge. Upon illumination, the LCE beam bends towards the light source due to temperature gradient along its thickness. As it surpasses the vertical position due to inertia, a self-shadowing effect is triggered, leading to cooling of the system. Despite energy dissipation from drag forces, the negative feedback resulting from self-shadowing injects energy into the system, initiating the self-oscillation phenomenon. Our investigation involves parametric studies exploring the impact of beam length, Young’s modulus, and light intensity on the oscillation's amplitude and frequency under illumination. Our findings indicate that shorter lengths or higher stiffness induce oscillations in the beam with the first mode of vibration. Conversely, longer lengths or reduced stiffness trigger the second mode of vibration. Additionally, applying higher light intensity increases the frequency of oscillation.

ABSTRACT. Shape memory polymers (SMPs) exhibit a distinctive capacity for significant deformations, followed by the restoration of their initial form upon exposure to particular external stimuli. This characteristic has enabled their recent use in many fields, particularly in biomedical devices and even for some aerospace applications. However, their use in structural applications has been limited due to their low strength and other mechanical properties. Incorporating reinforcing fibers into SMPs significantly enhances their mechanical properties though accompanied by a small reduction in their intrinsic shape memory properties. High glass transition temperatures (Tg) required for aircraft structural applications can be realized by optimizing the ratio of the SMP constituents. The current study is a finite element analysis based numerical investigation of the thermally stimulated response of glass fiber woven roving mat reinforced SMP laminate beams in terms of their deformation, shape fixity, and recovery. A 3D constitutive model for thermoset SMPs is implemented through a user-defined material (UMAT) subroutine in ABAQUS/Standard. The shape memory cycle begins at room temperature (Tl < Tg), heating to a high temperature (Th > Tg). After loading at high temperature (Th), the beam is cooled to low temperature (Tl) and then unloaded to assume a temporary shape. Upon reheating to high temperature (Th), it fully recovers its original state. The increase in strength of the SMPC and corresponding reduction in shape fixity were observed and quantified for different fiber volume fractions of the SMPC and compared with pure SMP. The study contributes valuable insight into optimizing SMPC structures for aerospace applications where a balance is required between high glass transition temperatures and high strength without much reduction in the shape memory effects.

ABSTRACT. Complex deformation and fracture events are of great importance for predictive modelling of materials in various applications. Among the existing approaches, discrete particle methods are versatile tools for tracking complex and arbitrary discontinuities. Yet, the continuum consistency of existing particle methods such as the Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH) and Peridynamics remains problematic. To resolve this, an innovative discrete particle method is here proposed that extracts the deformation gradient tensor at each particle from the kinematics of the particle's nearest neighbours. The resulting Continuum Bond Method (CBM), fully preserves the constitutive properties of conventional continuum models. Moreover, its discreteness preserves the powerful fracture characteristics of discrete particle methods. To demonstrate the capabilities of the CBM method, two examples are analysed. The first example is an elasto-plastic tensile bar subjected to large deformations. The results are assessed in direct comparison with a FEM reference solution, confirming the achieved discrete-continuum consistency. Further comparisons are made with typical SPH results, highlighting the violations in terms of continuum consistency for the latter. The second example focuses on complex fracture capabilities, for which a dynamic crack branching problem is considered.

The methodology is next applied to the micro-scale scratching of mono-crystalline silicon, whereby pressure-induced phase transformations are taken into account. The resulting model consists of a three-dimensional LAMMPS implementation of CBM combined with a phase transformation constitutive law for silicon. Cross-sectional TEM micrographs of silicon scratched with a sharp indenter, extracted from the literature, reveal a qualitative agreement with the simulated spatial phase distribution. Next, scratch experiments with a blunt indenter are executed and the surface profiles obtained with AFM are compared to the simulated ones for varying normal scratching forces. A qualitative agreement between the experimental and numerical post-scratch surfaces in the steady-state scratching regime is thereby achieved.

ABSTRACT. In order to determine the deformation response of materials and structures subjected to external loading conditions, classical continuum mechanics (CCM) was introduced by disregarding the atomistic structure. CCM has been successfully applied to numerous challenging problems. However, its governing equation faced a difficulty when there is any discontinuity in the structure such as a crack, since spatial partial derivatives in its governing equation are not defined for such a condition. In order to overcome this problem, a new continuum mechanics approach, Peridynamics (PD), was recently introduced with the intention that PD equations remain always valid whether there is any discontinuity in the structure or not. This character of PD makes this new approach a powerful tool for predicting crack initiation and propagation. Moreover, PD can be considered as the continuum version of molecular dynamics. Therefore, PD can be a suitable candidate for multi-scale analysis of materials. Furthermore, PD formulation can also be extended to other fields such as thermal diffusion, moisture diffusion, etc., so that it can be used as a single platform for multiphysics analysis of materials and structures with damage prediction capability. Hence, in this presentation, recent advances in peridynamics will be presented such as peridynamic computational homogenization and peridynamic differential operator.

ABSTRACT. Crack growth and propagation typically lead to the failure of brittle solids. Linear elastic fracture mechanics (LEFM) is commonly employed to model this process, quantifying a material's toughness through the critical stress intensity factor or the pre-factor of the singular stress field. Although widely accepted, this theory is designed for planar cracks, which contrasts with the geometrically complex nature of actual cracks. In this work, we examine the 3D kinematics of complex crack fronts using confocal microscopy on various transparent, brittle materials, including hydrogels with different chemistries and an elastomer. Our findings reveal a direct proportionality between the critical strain energy needed to drive the crack and the geodesic length of the crack, which makes the sample effectively tougher. The correlation between crack front geometry and toughness holds implications for the theoretical modeling of 3D cracks, and highlights an important gap in the current theory for 3D cracks.

ABSTRACT. Microstructure-scale interactions involving crystallographic texture (orientation and disorientation distributions), distributions of grain shape and size, nearest neighbor grains/phases, etc. in polycrystals can be simulated using the Crystal Plasticity Finite Element Method (CPFEM). Digital statistical volume element (SVE) instantiations that comprise a significant number of grains are analyzed by CPFEM to compute fatigue indicator parameters (FIPs) which are used as surrogate measures of the driving force for fatigue crack formation within the first grain or nucleant phase. The computed maximum FIPs usually increase in magnitude with larger numbers of realistic microstructure instantiations or SVEs analyzed. This work predicts the extreme value distribution (EVD) of the maximum FIPs associated with large engineering components comprised of up to 10^8 SVEs using a recent-developed upscaling scheme, based on statistical information identified from simulations involving only hundreds of SVEs, with each SVE containing nominally 264 grains. This scheme is numerically validated by extensive simulations for samples of duplex Ti-6Al-4V microstructure models with sharp transverse texture strained in two characteristic directions. The size of the training dataset for a reliable prediction is determined for different textures and loading directions based on uncertainty analysis. Finally, the statistical distribution of fatigue crack formation lifetime (FCFL) is correlated with the EVD of the maximum FIPs, facilitating quantitative exploration of the effect of crystallographic texture and sample size on the FCFL.

ABSTRACT. Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods.

ABSTRACT. This work focuses on damage tolerance study and fatigue life prediction of aeronautical parts. The goals are to understand fatigue small crack growth initiated from an artificially generated surface defect and to analyze the effects of the surrounding microstructure on the characteristics of the crack (path and velocity) and on the propagation mechanisms. The material of the study is a nickel-based superalloy used for the manufacturing of turbine disks in aircraft turbojets. It has been chosen to introduce an artificial defect on the surface of the specimen by electro-erosion. This approach is favored to fulfill dimensional constraints: obtaining the smallest experimentally feasible defect with dimensions greater than those of natural flaws and this without pronounced residual stress. Three grain sizes - ranging from conventional material (8µm) to hundreds of microns - are considered in order to better understand the influence of grain boundaries on crack growth and on dislocation mechanics. This is achieved with specific heat treatments (main phase grain growth control). Conventional propagation test methodology is extended to the small crack regime. We need to detect the crack initiation from the surface defect (20µm) and carry out the fatigue test up to the “long crack” regime. This requires the adaptation of the monitoring methods (electric potential, optical microscopy and images correlation, replica techniques) and of the cracking test protocols since we want to investigate incubation time and microstructural propagation threshold at given length (replacing respectively the pre-cracking and the decay research approaches). Those considerations lead to the utilization of a high frequency fatigue machine associated with high-speed camera. We will present results of the impact of the tests frequency (2 - 200Hz) on Paris law parameters and threshold values. Ultimately, the goal is to understand the role of the microstructural barriers and crystallographic orientations on the short crack regime.

ABSTRACT. Fretting is a phenomenon occurring between two contacting bodies in a mechanical system, potentially leading to crack initiation and consequential damage to the components. As shown by C. Montebello [1] and G. Rousseau [2], in partial slip conditions, stress intensity factors (SIFs) can be used to characterize the stress field around the contact edge independently of the geometries of the parts in contact. Experimental fretting tests conducted at different tangential load levels provided access to stress intensity factors through an integrated approach of digital image correlation (DIC). A sensitivity study was carried out to evaluate the impact on the measured stress intensity factors of a series of experimental parameters (zoom scale factor, outer radius of the ROI, inner radius of the ROI, size of the ROI mesh element, position of the ROI mesh, plane stress/strain state, first term of the Williams series and last term of the Williams series). The reference case study demonstrated, under different tangential loads, minimal impact of the zoom level on ΔK2 values. Among the analyzed parameters, the mesh size of the region of interest has the least influence on the ΔK2 result. Conversely, varying the remaining parameters by approximately 20% has an impact of around 5% on ΔK2 results. This observation underscores the remarkable robustness of the chosen approach for addressing the problem at hand.

ABSTRACT. Rolling Contact Fatigue (RCF) cracks in rails cause high maintenance costs and can reduce traffic safety. Hence, accurate predictions of RCF crack initiation are highly needed. Such predictions require reliable fatigue crack initiation criteria, depending on stress and strain histories. Thus, it is essential to use plasticity models that can accurately estimate the stress and strain states in rails, whose material properties evolve during rolling contact loading. In this contribution, a plasticity model with an anisotropic yield surface (based on Meyer and Menzel [1]) is calibrated against the previously conducted experiments with railway-like cyclic loading (compression and shear) on pearlitic R260 steel specimens. In these experiments, solid test bars were first predeformed in an axial-torsion machine to obtain different degrees of anisotropy. They were then re-machined into thin-walled tubular test bars and subjected to multiaxial cyclic loading. Based on the test results, material parameters are identified to describe the material behavior at different depths from the surface layer. The calibrated plasticity model is then used in the finite element simulations of realistic traffic situations to obtain accurate stress and strain histories. These are used to predict the number of cycles to macroscopic crack initiation in the rail surface layer using a newly developed RCF crack initiation criterion. This criterion accounts for the inhomogeneous stress-strain field in the surface layer and has been calibrated against three types of experiments: Large shear increments under different amounts of axial stresses (predeformation), strain-controlled low cycle fatigue tests after some levels of predeformation, and stress-controlled axial high cycle fatigue experiments. [1] K.A. Meyer and A. Menzel, “A distortional hardening model for finite plasticity,” Int. J. Solids and Struct., vol. 232, p. 111055, 2021

ABSTRACT. Osteoporosis (OP) is a skeletal disorder characterized by a decrease in bone mineral density (BMD) and a microarchitectural deterioration of the bone tissue, leading to increased bone fragility and risk of sudden fractures. One of the main problems of osteoporotic patients is their poor osteogenesis capability during bone regeneration processes, such as those occurring after fractures. The effects of mechanics on the newly formed bone, occur at the tissue, cellular, and even molecular scale. However, at all these scales, the identification of the mechanical parameters and their mechanisms of action are still unknown and continue to be investigated. This mechanical regulation of biological processes is the basis of mechanobiology and is used in this study to understand the multimodal response of the osteoporotic bone callus to external mechanical stimulation. An in vivo bone transport (BT) treatment was performed in the right-back metatarsus of three female merino sheep after a 30-week OP induction protocol to reach a 10% reduction in BMD. After the implantation of an instrumented external fixator, a 15-mm metatarsal defect was surgically induced. The BT process considers a latency period of 7 days, after which an electrical stimulation treatment was applied (5 h/day, 5 days/week) during the distraction and the consolidation phases till sacrifice, 40 days after surgery. In the distraction phase, a bone segment was gradually transported (1 mm/day) toward the position of the original bone defect for 15 days. Different monitoring techniques at the tissue and fibril scales (distraction forces measurement, gait analysis, ex vivo techniques) have been applied to simultaneously characterize the main biological and mechanical events in bone regeneration during osteoporosis. This work points out the unquestionable role mechanical and structural parameters play in the biological regulation of bone regeneration during osteoporosis.

ABSTRACT. Osteoarthritis is a painful joint disease characterized by progressive degeneration of the osteochondral unit's tissues with no possibility of reversing its progression once its onset. We may have identified one factor favoring this irreversibility: dissipative properties, i.e., the capacity to convert mechanical energy into heat. During our previous study, we made the important observation that degenerated cartilage does not possess high enough dissipative properties to allow its self-heating during mechanical stimulation. The temperature of degenerated cartilage culminates only to a maximum of around 33°C during physiological loadings compared to 37°C for healthy cartilage thanks to its preserved self-heating capability. Therefore, mechanical and thermal stimuli might play an essential role in cartilage homeostasis. Considering the thermomechanobiology aspect in cartilage, we will propose an original approach that may potentially change the therapeutical approach to treating early osteoarthritis.

ABSTRACT. Complete repair of cartilage defects caused by trauma or disease remains a significant clinical challenge due to the limited self-healing ability of cartilage. The development of biomimetic scaffolds that provide sufficient mechanical support and drive efficient mesenchymal stem cell (MSC) chondrogenic differentiation is critical for enhanced cartilage repair efficiency. In this study, we fabricated a 3D printed poly (glyceryl sebacate) (PGS) scaffold with dual porosity by salt fusion method and coated it with porous collagen I/II - hyaluronic acid (CI/II-HyA) framework to obtain a functionalized biomimetic composite scaffold with triple porosity. The PGS scaffold served as the mechanical support reinforcement and exhibited similar mechanical properties to the native cartilage, as well as excellent fatigue resistance similar to the joint tissue under physiological deformations. In in vitro tests, the presence of triple porosity increased cell loading efficiency and improved the metabolic activity of rat-derived MSC cells. More importantly, the combination of CI/II-HyA framework and PGS scaffold sustained an effective rat-derived MSC chondrogenic differentiation with an abundant de-novo cartilage-like matrix deposition by day 35. These results indicate that the biomimetic composite scaffold has the ability to support cartilage tissue growth and stimulate MSC cell proliferation and chondrogenic differentiation, showing great potential in cartilage defect repair.

ABSTRACT. This study explores the potential of biodegradable zinc (Zn) alloys to minimize the need for second surgeries in cardiovascular and bone implants. With a degradation rate in between the ones of magnesium and iron, our research aims to enhance Zn’s biological and mechanical properties through alloying. Twenty-one Zn alloys, manufactured using casting methodology, underwent thorough scientific screening. Six were binary alloys with a 0.8% wt of alloying element, Mg, Fe, Mn, Ca, Cu and Sr. The remaining materials were ternary alloys with 0.8% wt for the first alloying element and 0.5% wt for the second. Microstructural analysis employed scanning electron microscopy (SEM), energy dispersed X-ray spectroscopy (EDX), and X-ray diffraction (XRD). Results revealed a homogenized structure for the alloys with Mg, Mn and Cu, supported by superior mechanical performance. ZnMg alloy increased hardness by 53.7%, ZnMn by 78.7%, and ZnCu by 49.7%. Ternary alloys, such as ZnMgFe (168.2 %), ZnMgMn (143.3%), and ZnMgCu (141.2%), also exhibited improved mechanical properties over c.p. Zn. Electrochemical tests demonstrated reduced corrosion rates for the alloys compared to c.p. Zn, with values around 0.05 mm/year versus 0.15 mm/year for pure Zn. In the final screening stage, selected materials underwent biological characterization through cell viability assays with osteoblasts and endothelial cells. ZnMgFe, ZnMgMn and ZnMnFe emerged as promising for cardiovascular applications, showing no cytotoxicity with endothelial cells. For osteoblasts, ZnMn, ZnMgMn and ZnMnFe reduced the cytotoxicity of c.p. Zn. In summary, the alloyed Zn materials presented in this study demonstrate enhanced mechanical properties, reduced corrosion rates, and promising biocompatibility, suggesting their potential for advanced cardiovascular and bone implant applications.

ABSTRACT. Nowadays, to study in-situ or in operando the contact and friction behavior of an interface, measurements are mostly made through optical devices which requires the use of at least one optically transparent material and limit the analysis to only the evolution of the interface and more specially to the real contact area. Thus information outside this confined zone are most of time inaccessible. In this study, we overcame these two limits by using an X-ray Computed Tomography (XRCT). Starting from the very few pioneering studies, we adopted a more model approach to investigate by XRCT the classical laws of contact mechanics in a model sphere on plane contact. Our main objective was to examine the relationship between loading conditions, material properties, contact area and bulk deformation in 3D.

Thanks to an experimental loading device installed in a laboratory tomograph, we were able to obtain 3D images of a contact between a smooth PDMS sphere against a smooth PMMA plane for different loading conditions: pure normal loading/unloading (indentation) and shear loading under constant normal force (friction test). First, after segmentation of the 3D volumes, we extracted the evolution of real contact area and the surface displacement field of the PDMS specimen as function of the loading conditions (for indentation and friction tests). We then compared these evolutions to established experimental results and to the classical theoretical models of contact mechanics. Finally, we performed Digital Volume Correlation analysis by analyzing the displacement of dispersed particles that were inserted inside the PDMS sphere. We, thus, measured the 3D bulk displacement, strain and stress fields and compared them again with the prediction of theoretical models.

ABSTRACT. Aluminium alloys are widely considered by automakers to replace steel and meet the lightweighting demand to reduce CO2 emissions. New challenges remain to optimize their formability. This work focuses on a 6016 T4 aluminium alloy and to study strain heterogeneity leading to localization and final fracture under plane strain tension as this is the most critical strain state in stamping processes. Polycrystalline effects on the strain heterogeneity are investigated thanks to correlative 3D tomography, Digital Image Correlation (DIC) techniques within the material bulk and a digital twin finite element model of the tested specimen with grain information in the 3D volume. A miniaturized plane strain tensile specimen inspired by Park et al. [1] was developed and validated using 2D DIC on the specimen surface to verify the plane strain condition. The designed specimen was then tested in situ in a lab tomograph. Initially, a non-destructive acquisition of the three-dimensional grain map in the central region was performed using Diffraction Contrast Tomography (DCT) [2]. An in situ tensile test with Absorption Contrast Tomography (ACT) was then carried out in 12 increments up to fracture. The projection-DIC technique, based on projected 3D image contrast onto a 2D plane, was used to compute the real internal strain field in the specimen bulk, revealing a heterogeneous strain field with localization bands matching the fracture location. Subsequently, 2D generalized plane strain and 3D crystal plasticity simulations were performed using the measured grain map of the specimen. Simulated and experimental results are compared to investigate crystallographic effects on strain heterogeneity. [1] N. Park et al, “A new approach for fracture prediction considering general anisotropy of metal sheets,” Int. J. Plast., vol. 124, pp. 199–225, 2020 [2] F. Bachmann et al, “3D grain reconstruction from laboratory diffraction contrast tomography,” J. Appl. Crystallogr., vol. 52, Jun. 2019

ABSTRACT. Porous Mg scaffolds, manufactured through laser powder bed fusion (LPBF), hold potential for bone regeneration as they support tissue ingrowth and enable fluid transportation. Additionally, Mg implants can be fully re-absorbed by the human body, and they share mechanical properties with bone, which prevents stress shielding effects. Applying Mg scaffolds as a bone regeneration system requires detailed knowledge of the load-bearing capability during degradation. This property is investigated to obtain suitable mechanical strength and uniform stress distribution, the latter to ensure a smooth breaking mode.

LPBF-manufactured open porous cubic scaffolds of 10x10x10 mm3 of WE43 alloy with different lattice structures (BCC, FCC, TPMS), and an average strut diameter of 500 μm were surface modified by plasma electrolytic oxidation (PEO) to improve corrosion resistance and biocompatibility. The mechanical properties and fracture mechanisms are explored through in situ synchrotron X-ray microtomography compression tests conducted on both as-built scaffolds and those immersed in simulated body fluid for varied durations (7, 14, 21 days).

This study employs Digital Image Correlation (DIC) and Volume Correlation (DVC) techniques to delve deeper into the material mechanical behaviour. DIC and DVC provide a detailed analysis of localized deformations and strain fields across the scaffold structure. By scrutinizing the evolution of these parameters, we gain insights into the influence of corrosion on mechanical failure. This comprehensive approach enhances our understanding of the intricate interplay between material degradation and mechanical performance in the context of Mg scaffolds for bone regeneration.

ABSTRACT. Energy transition towards low-carbon energy sources, like renewable energies, has increased the interest of hydrogen as an energy carrier. However, its massive storage still remains a challenge. Underground seasonal storage of hydrocarbons in salt caverns, in use for decades, could be adapted to shorter term storage of hydrogen. However, cycles, adapted to the intermittency of renewable energies, represent short term thermomechanical cycling, which deserves a better understanding of the behaviour of rock salt, with specific focus on micro-damage development. Studies have focused on the mechanical behaviour of halite and have highlighted different deformation mechanisms, such as crystal plasticity, grain boundary sliding, micro-damage, grain boundary migration and diffusional mass. The constitutive relations inherently depend on their respective contributions to the overall strain, which depends on the stress state, the temperature and the mechanical loading rate, but also on the presence of brine. In this work we specifically focus on the development of micro-damage during compression tests, considering the effects of confining pressure and brine. Synthetic samples have been prepared in both dry and humid conditions. Compression tests at constant displacement rate at uniaxial and triaxial conditions were conducted, using a specifically designed triaxial cell transparent to X-rays. X-ray microcomputed tomography (XR-µCT) allowed us to perform time-resolved observations of the damage development during deformation. The 3D in situ observations are complemented with post mortem 2D microstructural investigations by SEM (scanning electron microscopy) and EBSD (electron back-scatter diffraction) analysis. The results suggest that dry material is prone to develop substantial micro-damage irrespective of confining pressure. The anisotropic crystal plasticity of NaCl generates plastic incompatibilities at grain boundaries, resulting in stress concentration and inter-granular micro-cracks, followed by interfacial shear sliding and further wing cracks damage. Conversely, the presence of brine appears to strongly reduce micro-damage development, most likely due to dissolution-precipitation related healing mechanisms.

ABSTRACT. This investigation employs an innovative in-situ EBSD/HRDIC technique for a thorough exploration of the complex twinning process in magnesium alloys. Utilizing multi-step in-situ deformation experiments, the study investigates grain orientation through in-situ electron backscatter diffraction (EBSD) and strain maps through high-resolution digital image correlation (HRDIC). The research delves into the intricate role of twin-twin interaction, addressing key questions regarding the twin ability of a grain, twin nucleation at grain boundaries, and twin variants selection among the six possible tension twins. In the course of in-situ tensile tests, it is revealed that grain boundaries exhibit more twin pairs than single twins, and contrary to conventional understanding, not all twin pairs result from twin transfer events. Instead, a predominant number of twin pairs at grain boundaries form through the co-nucleation of two twins in neighboring grains. A comprehensive statistical analysis, considering Schmid factors, geometric alignment of twin plane normal and shear directions, and the activity of basal slip in the parent grain, sheds light on twin transmission and co-nucleation across grain boundaries. This detailed investigation contributes significantly to advancing our understanding of deformation processes in magnesium alloys.

ABSTRACT. The equiatomic CoCrFeMnNi high entropy alloy (HEA) have shown an outstanding combination of mechanical properties not only at room temperature but also at cryogenic conditions. At room temperature, dislocation slip is the predominant deformation mechanism, however, under cryogenic conditions their mechanical response is dominated by extensive deformation twinning, which results in a significant increase in ductility, tensile strength and fracture toughness. This extensive mechanical twinning is attributed to their low stacking fault energy. Given the importance of twinning as a deformation mechanism for FCC HEAs, in-depth understanding and quantitative insights of the stresses required for its activation are crucial for advanced HEAs design. In this work, we aim to develop protocols to assess the critical resolved shear stress (CRSS) required for twinning to occur by applying in situ micromechanical testing. Therefore, three micromechanical geometries (micropillar, microcantilever and microshear) were chosen to activate deformation twinning in different stress conditions. Specific orientations to favor deformation twinning were carefully selected through electron backscatter diffraction (EBSD) analyses. Post-mortem analysis included scanning electron microscopy (SEM) imaging, EBSD and transmission electron microscopy (TEM) to verify if twin microstructure could be observed. It is found that deformation twinning was visible only in the pillars with CRSS exceeding 200 MPa, suggesting that the twinning stress for this HEA is close to 200 MPa at room temperature. A detailed analysis of the twinning stress and a comparison between three different micromechanical geometries will be discussed in the presentation.

ABSTRACT. As the lightest structural metals, there is strong motivation to study Magnesium alloys and expand their structural applications. A strong impediment is their complicated mechanical behavior with multiple twin and slip mechanisms. To develop predictive capability for these complex materials, fundamental scale modeling approaches are key. Recent full-field crystal plasticity models seek fidelity not only for the aggregate-averages but for the local fields with intragranular resolution. This in turn requires extensive experimental data at equivalent length scales for validation. We use an area-scanning version of the digital image correlation technique with optical microscopy to produce such data sets. By developing automated corrective measures in a custom setup, high resolution (numerical aperture) objectives are employed for maximal intragranular resolution while area-scanning allows data over a gross number of grains. The method has been applied in situ over finely spaced data points under monotonic and reversed load paths [1] for different textures of wrought Magnesium. Two phenomena are related to heavy microstructural strain localization observed in these materials. The more straightforward one is microstructural: Micro-texture bands, inherited from the previous forming processes have a considerable effect due to the extreme plastic anisotropy of Magnesium. The more sophisticated phenomenon is the coordinated propagation of twinning. This event is decisively texture dependent: rolled and extruded samples that show equivalent stress strain curves, in fact, deform with vastly different localization fields. The much sharper twin bands in rolled Magnesium are also intensely anisotropic. Recently, we have further guided these twinning bands with stress raisers and studied their enforced interaction [2]. Accordingly here, we cover multi-scale strain localization in wrought Magnesium with its dependencies on microstructure, load-path, and local deformation. [1] N. Shafaghi, E. Kapan, C.C. Aydıner, Exp Mech 60 (2020) 735–751. [2] S.C. Erman, L. Stainier, C.C. Aydıner, Mater Today Commun 35 (2023) 106203.

ABSTRACT. Hydrogen embrittlement in engineering materials poses significant practical and economic hazards and involves a number of different mechanisms, which depend on the specific microstructures of a material. In this study, we investigated the evolution of an initially smooth surface of a stable austenitic stainless steel under hydrogen exposure and the effect on the mechanical properties. The material was electrochemically charged for 120 h to achieve a significant hydrogen content. The effect of hydrogen was studied regarding lattice defects and the plastic deformation that prevails at the free surface. Based on Vegard’s law, an analytical model for hydrogen-induced resolved shear stresses on the different crystallographic planes was developed. This model explains the formation of slip lines and the occurrence of plastic deformation in the surface region. Nanoindentation was used to evaluate the effect of hydrogen charging and the related microstructural changes on the hardness and elastic modulus.

ABSTRACT. Mechanical surface treatments are commonly used in the aerospace industry to improve the surface properties and delay fatigue crack initiation of critical parts, such as turbine disks. SMAT (Surface Mechanical Attrition Treatment) is a process that creates a nanocrystalline layer on the surface of treated mechanical parts in addition to superficial compressive residual stress and strain hardening. Previous studies have shown that SMAT treatment can increase the yield strength, stress at failure, and fatigue life of metal parts by inducing severe plastic deformations at the material's surface without altering its chemical composition or core microstructure.

This study aims to investigate the effect of SMAT on the fatigue resistance of nickel-based superalloys in order to build a physically-based fatigue life model. The first stage focuses on precisely characterizing the impact of SMAT on the mechanical behavior of the material and its work-hardening mechanisms. To achieve this, an experimental study was conducted on Inconel 718 SMAT-treated specimens. In situ SEM 4-point bending tests were performed at 20°C and 450°C, combined with digital image correlation (DIC) based on a speckle pattern in order to access the local strain fields of the specimen. The resulting information was used to analyze the constitutive behavior along the SMAT-affected zone, up to a few hundred microns from the surface, in both tensile and compressive stress zones of the specimen.

In addition to the mechanical characterization, we investigated the gradient of material properties and their evolution under thermomechanical stress through microhardness measurements, crystal disorientation measurements using EBSD, and residual stress measurements using XRD. These complementary results allow the monitoring of the evolution of the SMAT induced properties under load cases representative of part service conditions.

Later on, fatigue tests will be conducted to study crack initiation mechanisms on SMAT-treated material, with particular attention given to the extrusion/intrusion phenomenon

ABSTRACT. We consider a heterogeneous elasticity problem and we show how to approximate it using a problem of the same type, but with effective constant coefficients that are defined by an optimization procedure. Our approach is based on the sole knowledge of the average displacement and stress at the boundary of the system, which are quantities that experimental measurements can provide. In the limit of infinitely small oscillations of the coefficients, we illustrate the links between this approach and the classical theory of homogenization. We also discuss comprehensive numerical tests and comparisons that show the practical interest of the approach.

This is joint work with Claude Le Bris and Simon Ruget (Ecole des Ponts and Inria).

ABSTRACT. A multi-scale framework is constructed for the computation of the stiffness tensors of an elastic strain-gradient continuum endowed with an anisotropic microstructure of arbitrarily-shaped particles. The influence of microstructural features on the macroscopic stiffness tensors is demonstrated by comparing the fourth-order, fifth order and sixth-order stiffness tensors obtained from macro-scale symmetry considerations to the stiffness tensors deduced from homogenizing the elastic response of the granular microstructure. Special attention is paid to systematically relating the particle properties to the probability density function describing their directional distribution, which allows to explicitly connect the level of anisotropy of the particle assembly to local variations in particle stiffness and morphology. The applicability of the multi-scale framework is exemplified by computing the stiffness tensors for various anisotropic granular media composed of equal-sized spheres. The number of independent coefficients of the homogenized stiffness tensors appears to be determined by the number of independent microstructural parameters, which are the local particle contact stiffness, the particle size and the fabric parameters, and is equal or less than the number of independent stiffness coefficients following from macro-scale symmetry considerations. Since the modelling framework has a general character, it can be applied to different higher-order granular continua and arbitrary types of material anisotropy.

ABSTRACT. Porous elastomers exhibit highly nonlinear and path-dependent material responses to large deformations. Predicting such complex behaviours analytically is unfeasible; therefore, traditional approaches often rely on test data to model these materials. Recent advancements in homogenization theory have enabled the development of high-fidelity predictions for complex material systems. Researchers have leveraged various machine learning techniques to establish constitutive models based on data containing homogenized material responses obtained from high-fidelity micromechanical simulations. In this research, we introduce a data-driven computational framework to implement surrogate constitutive models for porous elastomers undergoing large deformations. Explicit finite element (FE) simulations are conducted to compute the homogenised response of a cubic unit cell of an elastomer with constant initial porosity and material properties, subjected to a randomly imposed set of multiaxial strain states. The path-dependent stress response is predicted incrementally based on the current states of stress and strain, the prescribed strain increment, and the corresponding time increment. Average stress-strain measurements from FE simulations are utilized to assemble a training dataset for the surrogate macroscopic material model using simple neural networks. The prediction domain is gradually expanded to explore unseen initial porosities and material properties through active transfer learning. In addition to global stress predictions by the macroscopic surrogate model, the proposed framework approximates the corresponding local stress distribution in a porous unit cell via a coupled autoencoder architecture. The effectiveness of the proposed framework is demonstrated in producing material models with good accuracy and efficiency through several examples.