ABSTRACT. As a result of their high specific strength and stiffness, polymer-based composites are currently being used in a large variety of load-bearing applications where structural integrity and long-term durability is of the upmost importance. In the persistent pursuit for performance improvement, various reinforcements are added in the polymers, substantially affecting both short-term and long-term properties. A combination of a thermoplastic polymer matrix and short or long reinforcing fibers allows the use of injection moulding as a processing technique which, in turn, has increased production rates and facilitated the manufacturing of complex-shaped parts. This widespread use has led to an increased demand for the development of design tools that can predict the mechanical performance of such systems.

Unfortunately, there is an inherent complexity in the prediction of the mechanical performance of injection-moulded products based on fiber-reinforced thermoplastic polymers. The flow experienced during processing induces fibre orientation, which causes a pronounced directionality of mechanical properties (anisotropy). Moreover, the variation of flow conditions in the mould will lead to a spatial variation of these anisotropic properties throughout a product. Of course, the characteristic time- and temperature dependence of the polymer matrix introduces an additional complicating factor; specifically when there are several molecular deformation processes contributing.

In this study we took a previously developed anisotropic elasto-viscoplastic approach [1] and extended it to effectively describe the anisotropic, rate-dependent stress-strain response of a short-fiber filled polypropylene over a large range of strain rate and temperature (-25 to 100 C). The extension is based on experience in isotropic polymers [2] where the viscoelastic stress contribution of each molecular process is additively composed to the total response (multi-process, multi-relaxation time).

[1] A. Amiri Rad et al., Mech. Mater, 137 103141 (2019) [2] L.C.A. van Breemen et al.,J. Polym. Sci. B, 50, 1757-1771

ABSTRACT. In the context of the energy transition, the transportation sector faces the double challenge of producing light but high-performance structural parts while improving their recyclability. Thermoset-based composite materials allow the manufacturing of light structures with excellent mechanical properties, but are hardly recyclable and can only be processed via liquid molding techniques or prepreg consolidation. Moreover, high-rate composite processing is impossible with such matrices, as the necessary curing step often lasts few hours at a high temperature. Transitioning from thermoset to thermoplastic polymer matrix composites overcomes these shortcomings. However, the successful transition requires an understanding of the influence of processing conditions on the microstructure of the thermoplastic matrix and the mechanical performances of the composite.

Among thermoplastic polymers, semi-crystalline polymers like polyetheretherketone (PEEK) offer superior mechanical properties. However, their mechanical behavior is related to the amount and characteristics of the crystalline phase, which depend on the processing conditions. In this work, the effects of crystallization conditions (processing conditions and fiber proximity) on the microstructure and mechanical properties of ‘model’ carbon fiber-reinforced PEEK samples and of UD composite samples are investigated. The degree of crystallinity and crystalline phase morphology are first assessed. The mechanical properties of the PEEK matrix processed in different conditions and its resulting phases (inter-/intra-spherulitic and transcrystalline zones) are then evaluated via nanoindentation (NI) and atomic force microscopy (AFM). The local mechanical properties assessed by NI are later compared to the macroscopic mechanical ones obtained from transverse compression tests of thin composite specimens processed in the same conditions. In addition, the deformation and damage mechanisms occurring in the matrix at the micro-scale during transverse compression are studied using nano-digital image correlation (nano-DIC).

ABSTRACT. Polymer composites containing glass or carbon fibers (GFs o CFs) are extensively used in industries such as automotive, aeronautic, and civil engineering where there is a need for lightweight high-strength parts. These sectors often employ engineering polymers like polyetherimide (PEI), polyphenylene sulphide (PPS), and polyetheretheretheretherketone (PEEK) due to their excellent performance characteristics. However, with the increasing demand and economic value of these polymer composites, there is a growing interest in their recycling and revaluation [1,2]. Compared to the recycling of thermoset composites, the recycling of these polymer composites is relatively new and less developed [3]. Most research efforts have concentrated on mechanical recycling, neglecting chemical or thermal methods that require more energy and produce chemical waste [3]. Unfortunately, mechanical recycling technology faces challenges in preserving the fiber length, which in turn adversely affects the mechanical properties of the recycled materials and often results in downcycling. Thus, the present investigation is focused on evaluating the quality of recycled material obtained in the first cycle of mechanical recycling of short-GF reinforced PEI waste from injected parts designed to replace the metal parts of the aeronautical sector. Injected samples are prepared using recycled material (PEI and PEI reinforced with short GFs) to assess the effect of matrix and fibers on their mechanical properties (tensile, flexible and impact properties). Moreover, the content and length fibers are characterized to observe if there are changes after the recycling process.

ABSTRACT. Semi-crystalline polymers are heterogeneous materials with different structural scales. At the nanoscale, they are characterized by crystalline and amorphous phases arranged in a complex stacking of crystalline lamellae separated by the amorphous phase. These lamellae form a superstructure known as spherulite at the micrometer scale, significantly influencing the material's mechanical properties at all scales. However, the impact of each structural scale on macroscopic mechanical behavior remains unclear. This is primarily due to insufficient experimental testing and mechanical models, which capture the microstructure's mechanical properties and morphology at these scales.

This study investigates the quantitative elastic mechanical behavior of the spherulitic microstructure of semi-crystalline polymers at the nanometric and micrometric scales. Experimental methods utilizing indentation techniques with tips ranging from nanometers to micrometers were used. The novelty of this research lies in the similar experimental tests across the nanometric and micrometric scales, enabling comparisons between them.

A bulk sample of isotactic polypropylene (i-PP) was prepared to exhibit a spherulitic morphology, including on the surface, with spherulites having a mean diameter of ~120 µm. At the intra-spherulitic scale, nanoindentation (equivalent contact diameter ~1.4 µm) provided modulus mappings within several spherulites. The results reveal a modulus gradient between the stiffer center of the spherulites and their edges —attributed to spherulitic growth resulting in varying lamellae density across the branches of the spherulites. At the lamellar scale, elastic modulus maps obtained by AFM in mechanical mode (equivalent contact diameter ~20-40 nm) revealed heterogeneous moduli within branches of the spherulites, reflecting different local lamellar orientations. Across larger scales, from intra-spherulitic to spherulitic scales, nanoindentation tests demonstrated a decreasing modulus with increasing tested volume, eventually converging to a uniform value for indentation sizes in the tens of microns. This suggests that understanding the material's macroscopic mechanical behavior requires consideration of scales below this tested volume.

ABSTRACT. The mechanical properties of thermoplastic polymers strongly depend on processing conditions, which mainly affect molecular orientation, in the case of amorphous as well as semi-crystalline polymers. The use of orientation induced by processing is a current manufacturing trend to make products with outstanding properties. Therefore, it is of key importance to understand the relationship between microstructure, isotropic or oriented, and mechanical properties.

This work focuses on modeling concepts that capture the effects of molecular arrangements and orientation on the elasto-viscoplastic response of semi-crystalline isotactic polypropylene (iPP). The complexity of this problem lies in the polymorphic nature of iPP and the contribution of isotropic or oriented phases, both crystalline and amorphous, to the final material response. To investigate the different contributions to the total anisotropic response, a mean-field micromechanical model is used to link the structure to properties, accounting for the elasto-viscoplastic deformation of each constitutive phase and the texture evolution of the crystals. The crystalline phase is modeled with crystal viscoplasticity, and the so-called EGP model is used for the amorphous phase. The effect of anisotropy in the crystalline layer is naturally captured with the orientation distribution. The amorphous phase model was extended by combining modeling concepts developed for isotropic and oriented polymers, ending up with an anisotropic relaxation spectrum and a flow rule based on Hill’s stress.

The method is used to characterize the macroscopic response of semi-crystalline isotropic α-iPP. The response to tensile and compressive loading and the time-to-failure are well captured. The micromechanical model approach is also used to unravel the slip kinetics of β-iPP. Finally, the anisotropic version of the model is used to describe the elasto-viscoplastic behavior of an oriented film, containing mainly α crystals. The results capture the effect of loading angle and the strain rate dependence of the elastic and yield response.

ABSTRACT. Research in the field of architected materials has enabled engineered materials with mechanical properties that were previously thought unattainable. For instance, hollow truss-based lattices demonstrate high stiffness- and strength-to-weight ratios. However, these structures suffer from a bending-dominated response and stress concentrations at the sharp joints, the latter of which result in failure. Shell-based spinodal metamaterials have been proposed as an alternative to combat these stress concentrations due to their finite (low) curvature and bicontinuous morphologies. In particular, the mechanical properties of spinodal metamaterials can be tuned by introducing preferential interface directions which results in tailorable anisotropy.

In this study, we explore the effect of curvature and its anisotropic distribution on the stiffness and strength of spinodal metamaterials. The spinodal morphologies are generated using a computational spinodal decomposition framework where tunable anisotropy is introduced by energetically penalizing preferential directions for interface formation, resulting in a mean- and Gaussian-curvature distribution that is dependent on the direction of the surface normal. We propose a shell theory-based analytical framework to calculate the bending and stretching energies of these anisotropic shell-based spinodal morphologies and use this as a predictive metric for their direction-dependent relative stiffening and strengthening. Complemented by finite element models of the as-generated morphologies, we demonstrate a relation between curvature distributions and the stress distribution of these metamaterials. Furthermore, using a two-photon lithography process we fabricate prototypes of these anisotropic spinodal morphologies and perform in-situ nanomechanical uniaxial compression to determine their curvature-dependent stiffness and strength to further validate our analytical approach. Lastly, we extend the applicability of our analytical framework to other shell-based metamaterials such as triply periodic minimal surfaces (TMPS). Our findings present the potential of our analytical framework as an efficient tool for characterizing shell-based metamaterials to guide their curvature-dependent design.

ABSTRACT. Advancements in additive manufacturing have enabled fabrication of multi-functional architected meta-materials, allowing tailoring material properties (e.g., high stiffness-to-weight ratio) across a range of engineering applications including energy absorption, thermal insulation, and light weight structures such as sandwich panels in aerospace and automotive industries. Truss- and plate-based designs, the most common types of architected materials, are highly susceptible to stress concentrations, resulting in localized permanent damage. Therefore, there is a new paradigm shift towards spinodal shell-based architecture which avoids sharp joints to mitigate stress concentrations, and can therefore, achieve optimal stiffness while being particularly insensitive to defects. Due to their smooth, double curvature surface (e.g., eggshell), these shell lattices can be geometrically designed to control the anisotropic stiffness tensor and smoothly graded both as a function of relative density and topology. This provides a strong incentive to leverage their design capabilities to explore the effects on energy efficiency and wave guidance behaviour. In this work, both quasi-static and dynamic direct impact experiments are conducted on spinodal architectures to understand the role of strain-rate (~10^-4 – 10^2 s^-1) and topology on their mechanical behaviour. Specimens of different topologies (e.g., isotropic, columnar) and a constant relative density of 30% are manufactured using stereo-lithography with a tough resin. Through macroscopic load-displacement measurements, it was observed that these shell structures undergo more than 10x increase in strength when compressed dynamically, a feat unheard of in conventional architected materials. To further validate this, digital image correlation (DIC) is conducted to extract local surface-level displacement fields to explain the increased strain rate sensitivity and monitor the progression of local deformation modes (e.g., higher-order buckling) during compression. Lastly, these results are compared to experiments on conventional octet truss and sheet-based gyroid lattices, of the same material, to demonstrate the observed strain-rate sensitivity is indeed topology driven.

ABSTRACT. In this study an approach for reduced order modeling (ROM) of the dynamics of cellular micro-architectured media is presented. The method relies on the sparse structural topology of repeating unit cells and extracts the effective ROM parameters based on matching its eigenfrequency spectrum with the continuum analysis of the same system. The process involves matching kinetic and potential energy of the two low and high fidelity models as well as the modal shapes, for all frequencies up to a certain desired limit. The focus on low frequency resonant media makes the method particularly effective. While Bloch-Floquet periodicity is used in this initial step, the application to finite structures has shown great success in frequency domain analysis. Additionally, time domain analysis of finite structures can also be performed using the same parameters. The approach can be used for design of graded structures; in other words, perfect periodicity is not required and if neighboring cells have similar architecture, the ROM approach is still capable of satisfactory match with far more computationally expensive (e.g. 4 orders of magnitude) high fidelity models. It is observed, however, that exterior cells may require adjustments to their ROM parameters, especially in time domain (e.g. impact) applications. Other optimization approaches are discussed in improving the matching performance of ROM with continuum analysis.

ABSTRACT. The 2017-2027 Decadal Survey outlines the need for high-frequency antenna capabilities in CubeSat constellations, to aid Earth science objectives. Due to launch volume constraints, deployable structures become essential for antennas. Current solutions, like metallic mesh reflectors or reflect arrays, face limitations in lacking the stiffness to maintain surface accuracy for higher frequencies, prompting exploration of alternative technologies which have a deployable solid active surface. Structured fabrics, with compliant and jammed (stiff) modes, offer an alternative avenue. Leveraging this, we are developing a different deployable antenna architecture featuring a solid active surface with a pre-stretched elastic membrane as the multidirectional transformation mechanism. We explore a type of structured fabric that starts from a flat and foldable initial configuration, but upon release of the pretension, has a static equilibrium that achieves a desired three-dimensional shape. The computational design of the rigid tiles attached to these elastic sheets and their spatial distribution are optimized for specific fold lines and allows for a solid surface upon actuation. Upon releasing the pre-tensioned membrane, contracting forces on the tiles control the global structure shape through predetermined collisions at angles with neighboring tiles. The resulting local curvatures thereby control the global structure shape. This computational design approach was used to fabricate and demonstrate a paraboloid (resembling an antennae) of a desired focus, using a specific fold pattern that was previously designed to stowage an optical shield into a compact volume. The structured fabric design methods could be extended to designing deployments for other global target shapes and stowage volumes. Future exploration includes internal latticing for reduced structure density, kinematic mounts for deployment accuracy, and latching mechanisms for post-deployment stabilization.

ABSTRACT. Geared mechanical metamaterials were designed with an aim of maximising elastic strain energy absorption whilst conjointly reducing mass. Modular unit cells were initially designed to contain unmeshed spur gears arranged in parallel, and as using face-centred and body-centred profiles, and these were connected in continuum to loading plates using shafts positioned asymmetrically to generate small-deformation gear rotations. The gears mesh only when the unit cell is loaded and experiences deformation, and the gears thus contribute to load-resistance in the metamaterial unit cell, through tooth interlocking and gear-to-gear contact. Unit cells were parametrically designed using finite element analysis (FEA) methods to ascertain the optimal gear shapes and locations, optimal shaft dimensions and connection angles, and optimal global architectures enabling lightweighting. Care was taken to balance high strain energy storage and low mass to an optimum. Static compression tests were conducted on additively manufactured unit cells to validate the model outputs. Unit cells were subsequently built up into arrays, forming metamaterial structures, and these were tested and validated to ascertain the effects of scaling and modularisation on mechanical properties and behaviour.

ABSTRACT. Additive Manufacturing (AM), has the potential to revolutionize manufacturing processes for complex 3D, low production number components, to reduce part numbers, as well as to repair retired components. However the wider application of AM for high structural integrity components is in many cases limited by their unacceptable fatigue performance. This arises in large part from the entrainment of a variety of defects including loss of fusion defects and gas porosity. Here X-ray CT is applied to study the nature and location of AM defects according to the manufacturing process. Further it is used relate the fatigue life to the presence and location of critical defects, their potency and their behaviour. In particular, time resolved X-ray CT is used to track the behaviour of cracks initiated from different types of defects and used to assess and validate various models for fatigue crack growth and lifetime prediction.

ABSTRACT. Metallic additive manufacturing by Laser Powder bed Fusion enables the on-demand production of components with complex geometry and high added value. Despite its strengths, there are still challenges in fully understanding the interaction between laser and material. Energy density and normalized enthalpy are crucial factors to predict and control the overall process. When the energy density reaches a sufficient level, a specific state is attained: the keyhole regime. In this scenario, the melt pool forms a deep and narrow cavity, and intense competition occurs within it. This regime is inherently unstable and prone to collapse, often resulting in the formation of characteristic pores. In this study, the 316L powder is used. Single tracks were generated to explore the boundaries of the keyhole domain. A process window was defined by adjusting power, scanning speed, and spot size parameters. However, the interaction between laser and material differs significantly between single tracks and multiple tracks due to the changes in interaction dynamics. In a single track, the laser only interacts with the powder on the both sides of the edificated seal. In contrast, for multiple tracks, the laser also interacts with the previously laid tracks. This underscores the inadequacy of characterizing only a single track for a comprehensive understanding of the interactions. Hence, this works aims at characterizing the melt pool during the formation of different sample construction: single tracks, multiple tracks on the same layer, and tracks between several layers. The purpose is to understand how the interaction between laser and material evolves on different successive tracks and layers. Various sets of keyhole processing parameters were chosen to fully understand the range of keyhole process windows. The assessments involve dimensions of the melt pools through metallographic measurement, characterization of pores formation through micro-tomography and the evolution of microstructures through EBSD measurement.

ABSTRACT. Additive manufacturing parts process specific microstructures related to the specific thermal conditions undergone during the process. Process parameters have substantial impact on the resulting microstructure which partly influence the mechanical behavior of the final part. Targeting microstructures could be expected in a matter of optimization. To achieve, thermal activity is a suitable gateway bridging process parameters and microstructure while monitoring it in-situ.

Cellular Automaton models are widely used to simulate solidification process during additive manufacturing, often coupled with finite element methods to compute thermal activity within the melt pool. However the computational cost remains significant particulary for large simulations limiting their practical use in experimental design.

In this study, a two-color pyrometer and a monochromatic infrared camera are coupled together and setup during Direct Energy Desposition (DED) process. Temperature field near the melt pool is observed, providing appropriate insights for microstucture prediction such as cooling rates, thermal gradients and melt pool shape.

Recently, we have developed a new fast model for microstructure prediction based on upscaling complexe phenomena taking place at the scale of the solidification process into simpler evolution laws. This new approach reduces the degree of freedom from O(n^3) to O(3n) in 3D. As the resulting microstructure is strongly correlated to the unknown microstructure of the subratre upon which the epitaxial growth takes place, the proposed approach leads to a statistical analysis of the microstructure resulting from the solidification process.

Understanding the relationship between thermal activity and microstrcuture, the previous infrared sensors become suitable tools for in-situ monitoring of the process and control it.

ABSTRACT. The solid-state additive manufacturing (AM) process of Multi-Layer Friction Surfacing (MLFS) is ideal for building 3-dimensional parts made of precipitation hardened high-strength 7075 aluminium alloy. 7xxx aluminium alloys have the advantage of high performances to weight ratio but 7xxx series are still a challenge to process using fusion-based AM processes. That is why, MLFS is a good candidate for high quality part building by avoiding solidification defects. This process leads to produce microstructural (grain size and precipitate size and distribution) and mechanical (hardness) heterogeneities.

The thermal history is studied using a multilayer thermal model, including temperature, cooling rate and heat accumulation simulations, that provides a better understanding of the effect of multiple thermal cycles on microstructural heterogeneities. The grain size evolution in a layer shows small grains in the layer centre with even finer grains at the bottom and top of the layer. Indeed, feedstock material grains are fully recrystallized and refined. The grain size profile also varies along the deposition height of the multi-layer structure. These variations with height result from a combination of mechanical and thermal effects during MLFS. The strengthening precipitates are significantly affected in the layered structure due to the complex thermal field. The size and density gradients of the precipitates along the height of the structure is responsible for the significantly higher microhardness of the top layer.

For some applications homogeneous parts are required. Using post-MLFS T6 heat treatment, the hardening precipitation is restored, improving significantly the microhardness. The microhardness profile is uniform and reaches the peak-aged T6 state stage. Abnormal grain growth occurs during the T6 heat treatment. However, tensile properties are restored to 7075 classical T6 values, as tensile specimens show strength exceeding 500MPa and a typical elongation of 10%.

ABSTRACT. 316L stainless steel (316L) with 0.5wt% Si and 2.3wt% Si were fabricated using laser direct energy deposition (LDED). A stark difference is found in the density of ∑3 twins and fine grains in the microstructures of the two materials. 316L with 2.3wt% Si exhibits a remarkably high percentage (23%) of ∑3 twin boundaries whereas 316L with 0.5wt% Si exhibits very low (less than 3%) of these boundaries. In this work, we aim to understand the origin of this difference. EBSD analysis of 316L with 2.3wt% Si reveals that clusters of twins exhibiting shared <110> five-fold symmetry axes are present in the microstructure, which suggests that they formed via the icosahedral short-range order (ISRO)-mediated nucleation during solidification [1]. Additionally, twins form during grain growth due to an ISRO-induced stacking fault mechanism, as evidenced by twin variant analysis showing more than 3 variants, which cannot occur during nucleation from one ISRO motif. This result is surprising because ISRO-based mechanisms have been mainly reported in face-centered cubic alloys printed via laser-powder bed fusion. In this talk, we will demonstrate why and how these mechanisms can occur in LDED 316L. [1] M. Rappaz, Ph. Jarry, G. Kurtuldu, J. Zollinger, Metall. Mater. Trans. A 51 (2020) 2651–2664.

ABSTRACT. Additive manufacturing of metallic materials enables the design of functionally graded materials (FGMs) that exhibit a gradual change of chemical composition within the same part. This comes as a great option for dealing with dissimilar joints or for creating location-specific properties (and/or functionality). Here, we investigate material compatibility and explore processing parameters for parts graded from a stainless steel 316L and a Ni-based superalloy IN718. We combine (1) advanced characterization (SEM, EDX, EBSD, micro & macro hardness, X-ray tomography and diffraction) of print quality, microstructure and properties of graded samples manufactured by direct energy deposition (DED) technique and (2) computational thermodynamics (CalPhaD) exploration of phase diagrams and assessment of thermal properties along the material gradient. We explore the fundamental mechanisms of microstructure selection and properties in metallic FGMs and investigate the appearance of defects, e.g. (micro-)cracks, and phases/constituents in specific regions of the compositional gradient. By doing so, we look to establish a robust pathway for the design, manufacture, and characterization of metallic graded materials for several industrial applications – here, specifically oriented toward enhancing the local resistance to thermal cycling in steelmaking components.

ABSTRACT. The fracture behaviour of a material composed of spherical soft inclusions in a matrix is studied numerically. To this purpose a phase field model of dynamic crack propagation is used and the statistical nature of the disorder is varied (from a random distribution with simple hard sphere exclusion to a more uniform distribution of inclusions).

While for high speed crack propagation, effects of the nature of disorder is small, it is seen that close to propagation threshold the nature of the disorder can have significant effects: The more uniform the inclusion distribution the lower the apparent fracture energy is.

ABSTRACT. Sea-level rise is one of the most critical issues the world faces under global warming. However, the accuracy of sea-level rise projections is compromised by the crude, empirical laws used to characterise mass loss from glaciers and ice sheets, the phenomenon that constitutes the largest contributor to sea-level rise. There is a need for physically-based computational models capable of predicting iceberg calving due to hydrofracture, one of the most prominent yet less understood glacial mass processes. In this work, we have developed a phase field fracture formulation capable of predicting the growth of crevasses (deep crack-like defects) and subsequent iceberg calving, as well as the role that increasing meltwater plays in accelerating these phenomena. The potential of the computational framework presented is demonstrated by addressing a number of 2D and 3D case studies, involving single and multiple crevasses, and considering both grounded and floating conditions. The model results show a good agreement with analytical approaches when particularised to the idealised scenarios where these are relevant. More importantly, we demonstrate how the model can be used to provide the first computational predictions of crevasse interactions in floating ice shelves and 3D ice sheets, shedding new light on these phenomena. Also, the creep-assisted nucleation and growth of crevasses is simulated in a realistic geometry, corresponding to the Helheim glacier. The computational framework presented opens new horizons in the modelling of iceberg calving and can be readily incorporated into numerical ice sheet models for projecting sea-level rise.

ABSTRACT. We present a new numerical method for dynamic fracture at small strains which is based on a discontinuous Galerkin approximation of a first-order formulation for elastic waves and where the fracture is approximated by a phase field driven by a stress based fracture criterion. The staggered algorithm in time combines the implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase field evolution. Then, driven by the fracture criterion, the material is degradated, and the waves are reflected at the diffusive interface. We demonstrate in 2D and 3D applications the dynamic fracture evolution with multiple fractures initiated by reflections.

Then we discuss the extension to visco-elastic materials and different energy based elastic driving forces. Here we show that the first-order approach extends to visco-elastic materials and remains stable also in the limit of very small viscosity.

Finally, the phase field approximation of wave-induced fracture phenomena is compared with results obtained by continuum-kinematics-based peridynamics.

Weinberg, K. and Wieners, C. (2022): Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves. Computer Methods in Applied Mechanics and Engineering, 389, 114330.

Partmann, K., Wieners, C. and Weinberg, K. (2023): Continuum-kinematics-based peridynamics and phase-field approximation of non-local dynamic fracture. International Journal of Fracture, 244(1), 187-200.

ABSTRACT. A pivotal aspect in the application of phase-field theories is the decomposition (or, split) of the strain energy density into tensile and compressive components, crucial for preventing the interpenetration of crack surfaces and ensuring the physical fidelity of predicted crack paths. While popular methods such as spectral decompositions and hydrostatic-deviatoric decompositions are employed for this purpose, challenges arise in effectively handling crack growth in compression, prompting the exploration of alternative decomposition schemes.

A recently suggested model [1], inspired by the classical Mohr-Coulomb fracture criterion, combines the spectral and the hydrostatic-deviatoric splits to address the shortcomings of existing methods. To assess its efficacy, a series of global compression tests induced by impacts were conducted on brittle gypsum plaster specimens with embedded flaws and holes. Crack developments in these impact experiments were meticulously monitored using a high-speed camera. Dynamic phase-field finite element simulations were conducted using the aforementioned model and compared to the experimental results. The outcome dictates a commendable agreement between the model and the experiments, implying that the model is capable of capturing rapid transient effects in isotropic brittle materials subject to global compression induced by impacts emphasizing the model's potential to offer mechanistic insights into the dynamic mixed-mode fracture in brittle materials.

[1] Hesammokri P, Yu H, Isaksson P (2023). An extended hydrostatic–deviatoric strain energy density decomposition for phase-field fracture theories. Int J Solids Structures 262-263: 112080. https://doi.org/10.1016/j.ijsolstr.2022.112080

ABSTRACT. Failure of engineering components made from metals is often preceded by the development of significant plastic strains. For the life span prediction of such components, it is important to understand the details of the fracture process. This particularly includes the interaction between the development of plastic deformation and damage on a microstructural level, leading to microscopic cracks which ultimately evolve into macroscopic cracks and then cause structural failure.

This study addresses ductile fracture of single grains in metals by modeling the nucleation and propagation of transgranular cracks. We present a model that integrates gradient-enhanced hardening, phase-field modeling for fracture, and crystal plasticity, presented in a thermodynamic framework within large deformation kinematics. The phase-field model employs a micromorphic formulation that is used for assuring irreversibility upon unloading.

We present ability of the model to predict the influence that grain boundaries and other obstacles have on transgranular crack growth. Therefore, we study the size effects introduced by the length-scale parameters in the gradient-enhanced hardening and phase-field models. Furthermore, it is demonstrated that the model is able to handle loading-unloading situations. Finally, we provide an example of how the presented model handles material inhomogeneities, such as inclusions arising during casting. Numerical examples are provided both in 2D and 3D.

ABSTRACT. The propagation of short cracks in FCC metals is strongly influenced by microstructures, in particular associated with the linear defects of the crystals, i.e. dislocations.

In this work, a new coupling between two methods at the mesoscale is proposed to investigate the interaction of moving cracks with three-dimensional dislocation microstructures. First, crack propagation is predicted by a phase field model. In this approach, cracks are described by some continuous damage field that evolves so as to minimize the total free energy, including stored elastic energy and surface energy associated with the crack. Second, dislocation microstructures are handled by a Discrete Dislocation Dynamics (DDD) model that describes plastic deformation by the movement of dislocations under external loading.

To couple both models, the DCM (Discrete-Continuous Model) approach is used, where dislocations are described by continuous fields (eigenstrain or Nye tensor) in an elastic solver. Fast Fourier Transform (FFT) based solvers are used for their computational efficiency. Particular discretization schemes have been adopted to minimize the smoothing of dislocation cores, usually performed in DCM approaches. The different schemes are carefully analyzed with respect to the quality of the predicted fields. In addition, the resulting model is implemented using efficient parallelization solutions.

Thanks to this new coupling, we have been able to study the elastic shielding on crack propagation according to the nature of the slip systems and the dislocations density. We have also been able to investigate phenomena and ingredients rarely accounted for, such as dislocation cross slips close to the crack front or the influence of the number of sources. This mesoscale method constitutes a breakthrough for the thorough analysis of physical mechanisms controlling the early stages of fracture in metallic materials.

ABSTRACT. The determination of the onset of void coalescence is critical to the modelling of ductile fracture in metallic alloys. Most numerical models rely on analyses of single defect cells, and therefore underestimate the void interactions. This study provides an analysis of the response of microstructures with random distributions of voids to various loading conditions.Cells embedding a random distribution of identical spherical voids are generated within an elastoplastic matrix and subjected to a macroscopic loading with constant stress triaxiality and Lode parameter under periodic boundary conditions in finite element simulations. The strain field developing in random microstructures and the one in unit cells are shown to feature distinct dependencies on the Lode parameter L owing to different failure modes. The cell may fail in extension (coalescence) or in shear. Moreover the random void populations lead to a significant dispersion of failure strain, which is present even in simulations with high numbers of voids. Strain localization is detected in the simulations using Rice’s criterion computed at the cell level. This criterion is shown to capture the onset of localization and the type of failure mode, either extension or shear banding. Moreover, the influence of the loading orientation, i.e. the orientation of the principal axes of the applied stress tensor with respect to the microstructure cube, is systematically studied. Significant anisotropy of failure behavior is observed, especially in the case of single void unit cells, which can be attributed to the intrinsic anisotropy of the simulation cells. Finally minimal failure strain values at localization with respect to all loading orientations are found. A zone of reduced ductility is observed under generalized shear loading conditions [1]. [1] C. Cadet, J. Besson, S. Flouriot, S. Forest, P. Kerfriden, L. Lacourt, V. de Rancourt, Journal of the Mechanics and Physics of Solids 166, 104933, 2022. doi:10.1016/j.jmps.2022.104933

ABSTRACT. Ductile fracture of structural metal alloys is commonly associated with the nucleation, growth, and coalescence of microscopic voids. In high-strength 6000-series aluminium alloys, the iron-rich constituent particles formed during solidification are often responsible for failure initiation. The constituent particles have various shapes and sizes, ranging from less than one to several micrometres. Micromechanics-based numerical studies are usually based on unit cell simulations where the microstructure is idealized as a spatially uniform distribution of equal-sized voids. However, unit cell models cannot account for effects emerging due to varying particle sizes that could be significant for strain localization and ductile failure. The current work is devoted to examining how the heterogeneity due to realistic particle size distributions influences the failure strains predicted using micromechanics-based models. To this end, we conduct finite element simulations using models containing many voids sampled from a log-normal size distribution. Statistically representative void samples cannot be resolved in 3D finite element models. Assuming that the voids are regularly spaced, a cost-effective modelling alternative is to describe each by a porous plasticity model. The validity of this approximation is assessed by comparison with simulations of models where the voids are spatially resolved. Consequently, simulations of 2D plane strain models containing many voids are conducted using both modelling approaches. The simulations exhibit a large variation in the macroscopic response after peak stress due to the void size-induced heterogeneity. Failure is expedited and there is less variation in failure strain when more voids are included. A key result is that the models using a homogenized void description give similar results as simulations using spatially resolved voids while reducing the computational runtimes by several orders of magnitude. This opens for 3D simulations of microstructures with statistically representative particle size distributions.

ABSTRACT. Under high strain-rate loading conditions like in plate impact experiments, material failure may happen by spallation, i.e. a damage process due to localized tensile stress states generated by interacting release waves. For ductile materials, the failure process is commonly divided in nucleation, growth and coalescence stages. A key component of the modeling of spallation is the representation of the growth stage with a Gurson-like model. Adding a description of nucleation requires determining void nucleation statistics, for instance through post-mortem microscopic observations; yet such analyses are difficult and require careful recovery of specimens. Another approach would be to directly estimate nucleation statistics from more easily available macrocopic measurements such as the evolution of free surface velocity (FSV).

We propose to calibrate three ductile failure models from plate impact experiments on tantalum using only FSV data. The first model only describes growth (with an initial porosity free parameter), whereas the two other models add nucleation, through a Weibull density describing critical nucleation stress dispersion (either with all Weibull parameters kept free for identification, or through a simplified version with some fixed parameters). A Bayesian calibration approach is used (with Openturns software), so as to quantify uncertainties for the identified model parameter values.

More precisely, for each reference experiment, a limited number of simulations with different parameters are performed using a hydrodynamical code. From the simulations, characteristic points (the first minima and maxima of the free surface velocity) are extracted, so as to train Gaussian Process metamodels. A Bayesian calibration comparing the metamodels to the experimental results, using Markov Chain Monte Carlo sampling, finally provides posterior distributions for each model parameter. The calibration results are used to assess to what extent the nucleation models can be reliably identified from pure macroscopic data.

ABSTRACT. To predict the limit load and onset of failure of a part under a given load, knowledge of the points of stress and strain localisation is crucial. Reasons for strain localisation can be macroscopic, such as the part's geometry. However, strain localisation can also be a result of microscopic features like material morphology. Considering heterogeneous solids with voids, strain localisation occurs in the form of shear bands that depend on the potentially non-uniform void distribution. Hence, predicting the onset of damage and failure in parts featuring a non-uniform void distribution may require resolving their microstructure. However, high-resolution micromechanical methods capable of doing that are restricted to the microscale due to high computational costs. In this contribution, the aim is to assess the strain localisation due to shear banding in representations of 2D random microstructures with a given porosity through an upper bound limit analysis method at reduced computational cost compared to other micromechanical approaches. The model domain is discretised using rigid elements. Deformation and energy dissipation are restrained to discontinuities of the velocity field introduced at element boundaries. Previous work of the authors established that the Delaunay triangulation of the considered microstructures features edges that coincide with the locations of shear bands when the void centroids serve as the nodal grid. Based on this finding, the model domain is discretised via Delaunay triangulation with the discontinuities introduced along element boundaries representing potential locations of shear bands as narrow zones of strain localisation and plastic dissipation. This discretisation approach efficiently and effectively reduces the number of potential discontinuities, thus further lowering the computational cost of the analysis method. To demonstrate the approach's capabilities, predicted limit loads under uniaxial tension and deformation patterns in representations of random periodic microstructures are compared to results from a finite element study.

ABSTRACT. The essential work of fracture (EWF) has been used for long to characterise the cracking resistance of thin ductile sheet metals. The EWF corresponds to the plastic and fracture dissipation per unit crack surface spent in the fracture process zone (FPZ), where necking and damage occur. To experimentally extract EWF, pre-cracked thin specimens with different ligament lengths are loaded until full fracture. The energy expenditure can be separated into a diffused plastic zone (DPZ) and a localised FPZ. Because the plastic dissipations in these zones scale differently, they can be separated using geometrically similar specimens with different ligament lengths, e.g. double edge notched tension (DENT) specimens. As a result, the EWF is extracted as the dissipation per surface area spent in FPZ, averaged over the entire crack propagation. The main drawback of the EWF method is with the need for using many geometrically similar specimens of different sizes.

The objective of this study is to perform full 3D finite element simulations of DENT specimens with a micromechanics-based ductile fracture model to determine the EWF and to explore the major factors affecting the EWF. A recently developed nonlocal advanced Gurson-based model [1] is used for this purpose and applied to several materials. For each material, the parameters are first identified and then validated with the corresponding experimental data. Next, geometrically similar DENT specimens with a wide range of ligaments as well as thicknesses are simulated to extract EWF as a function of the material parameters and thickness. The results, among others, essentially confirm the empirical rules of validity for the EWF, now rooted on a fundamental micromechanics-based analysis.

References: [1] https://doi.org/10.1016/j.jmps.2020.103891

ABSTRACT. Digital image correlation has emerged as a convenient approach in characterizing and measuring the fracture parameters mostly for thin specimens. This presentation presents an approach to extend the digital image correlation to determine the energy release rate and to quantify the evolution of the through-thick crack size under increasing load in thick metallic specimens. This presentation first introduces the theoretical basis, which allows the characterization of the through-thickness average energy release rate through the displacement, strain and stress fields determined from the specimen surface, followed by experimental validations. Following that, this presentation proposes a normalization method, directly measurable by digital image correlation, to quantify the evolution of through-thickness crack size, based on optimal correlations. The proposed approach enables sizing of cracks in specimens with two crack fronts, e.g., the middle tension crack specimen. Comparison against the experimental results demonstrates the promising potential of the contactless method in quantifying the fracture resistance curves for various types of thick specimens.

ABSTRACT. Structural instability is one of the major causes of degradation in layered structures such as nickel-manganese-cobalt-oxide (NMC) and it mainly happens due to the anisotropic volume change in these high-capacity cathode active material for lithium-ion batteries during cycling and limits their widespread application despite high energy density. Here an anisotropic chemo-mechanically coupled model is implemented in 3-dimensions to simulate the electrochemical performance and fracture in polycrystalline cathode active material, where a two-way coupling between the mechanics and diffusion is employed and the damage at the grain boundaries is modeled using a cohesive zone model. Furthermore the wetting of the freshly cracked surfaces by the electrolyte is also considered in the model and we studied the impact of electrolyte penetration into the cracks. Due to the anisotropic material properties of layered structures such as NMC, the effect of crystallographic orientation of grains on electrochemical performance and cracking of active material is investigated, where orientations based on electron backscatter diffraction measurements are employed. Furthermore, the impact of primary and secondary particle's size, and grain morphology are studied. Results suggests that the electrolyte penetration into the cracks enhances the Li transport and electrochemical performance. Moreover, secondary active material particles with smaller and radially elongated grains alleviate the mechanical damage better.

ABSTRACT. Silicon electrodes for lithium-ion batteries exhibit a theoretical capacity ten times higher than that of graphite electrodes currently used in commercial systems. When lithiated/delithiated, silicon experiences stresses on the order of one GPa, thus inducing damage in the material which results in poor cyclability. Irreversible continuum thermodynamics predicts that these stresses affect the lithiation itself in different ways for monophasic and biphasic lithiation (progressive invasion of the electrode by a lithiated phase of given composition) [1]. When lithiation takes place homogeneously (without phase transformation), mechanical stresses affect lithiation through their effect on the chemical potential of diffusing lithium (Larché-Cahn theory). This coupling has first been probed experimentally in homogeneous lithiation using a method where the stress state of silicon is modified indirectly through incremental delithiation [2].

On the other hand, we investigate here the coupling through a converse experiment by imposing mechanical loading at various lithiation rates and measuring the effect on the electrochemical response of an amorphous silicon thin film, deposited on a stainless-steel substrate. This mechanical loading is applied by deforming elastically the steel substrate of the silicon thin film, which allows to directly probe the contribution of mechanics to the lithiation/delithiation processes. Under galvanostatic conditions, incremental changes in stress lead to instantaneous change in the electrode potential, followed by its relaxation. Experimental results from uniaxial tensile tests show that an applied strain of 0.3%, resulting in changes in stress in silicon of ~200-300 MPa, induces a potential variation of about 2.5 mV. These experimental results have more recently been modeled through the use of a viscoplastic flow rule for the amorphous material, which captures both this instantaneous change in the electrochemical potential and its subsequent relaxatios, confirming previous modeling choices.

[1] Bower, Chason, Guduru, Sheldon, Acta Mater. (2015) [2] Sethuraman, Srinivasan, Bower, Guduru, J. Electrochem. Soc. (2010)

ABSTRACT. A novel numerical framework based on FFT solvers is proposed to simulate fracture at themesoscale in chemo-mechanical processes. The modeling approach is based on the phase-field fracture model integrated into a chemo-mechanical solver in finite strain. The simulations rely on an implicit staggered approach in which the three coupled problems are solved sequentially until reaching convergence. This FFT framework has been validated against finite element solutions in different cases and the computational cost has also been studied. The resulting framework has excellent performance and allows to resolve problems on representative volume elements of realistic three-dimensional microstructures.

The method has been parameterized to simulate the chemo-mechanical damage occurring in the active particles of ion-lithium batteries. In these particles, the intercalation and deintercalation cycles in the electrode particles lead to the initiation and propagation of cracks which degrades their behavior. The method proposed was able to simulate the response until the failure of irregular shape particles in three dimensions showing degradation and cracking patterns similar to the ones obtained in experiments.

ABSTRACT. The presentation introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws.

Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. To consider more general irreversible processes such as thermo-elasticity and thermo-visco-plasticity, incorporation of the first law of thermodynamics, expressed in terms of the entropy density, will be introduced as an additional conservation law.

For spatial discretisation, a vertex-based Finite Volume method and a Smooth Particle Hydrodynamics alternative are employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Ballistic energy of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework, including high velocity impact thermally coupled scenarios.

ABSTRACT. Carbon-fibre reinforced epoxy polymer (CFRP) composite materials are widely used in aeronautical cold structures, such as wings, empennages, fuselages: in aero-engine applications, fan blades CFRP may be subjected to particularly harsh environmental conditions, since temperatures can be as high as 150°C, and the flow speed can be in the range of Mach 1.

It is widely known (see for instance [1]) that epoxy polymers are subjected to thermo-oxidation phenomena when exposed to high temperatures, that is, a coupled diffusion-reaction of oxygen within the macromolecular polymer leading to color change, material antiplasticization and embrittlement, development of shrinkage strain due to the departure of reaction volatile products. So far, aging tests have only been conducted in oven settings under static air, which provides a detailed understanding of the phenomenon. The present study aims to improve the understanding of the coupling between airflow and material degradation, by exploring the effect of airflow temperature and speed on thermo-oxidation phenomena. The hot airflow at high speed may lead to energy exchanges with the polymer sample, leading to heating and thermo-oxidation diffusion-reaction phenomena, ultimately affecting color and material property changes, polymer shrinkage and degradation. Samples were aged in oven and in specific BATH setup able to simulate an air flow at high temperature and high speed. Several experimental techniques (color change measurement by optical measurements under microscope or material property change measurement by nanoindentation) were used to analyze material degradation, and to explore the impact of airflow. Aero-thermo-chemo-mechanical coupled models were employed to enhance the understanding of the complex experimental scenario.

The presentation will focus on the chemico-mechanical coupling using Neural Network.

[1] Celina, Mathew C., Review of polymer oxidation and its relationship with materials performance and lifetime prediction (2013), Polymer Degradation and Stability, Vol.98, No.12, p.2419-2429

ABSTRACT. We present a patient-specific finite element model of the human cornea that accounts for the presence of the epithelium. The thin anterior layer that protects the cornea from the external actions has a scant relevance from the mechanical point of view and it has been neglected in most numerical models of the cornea, which assign to the entire cornea the mechanical properties of the stroma. Yet, modern corneal topographers capture the geometry of the epithelium, which can be naturally included into a patient-specific solid model of the cornea, treated as a multi-layer solid. For numerical applications, the presence of a thin layer on the anterior cornea requires a finer discretization and the definition of two constitutive models (including the corresponding properties) for stroma and epithelium. In this study we want to assess the relevance of the inclusion of the epithelium in the model of the cornea, by analyzing the effects in terms of uncertainties of the mechanical properties, stress distribution across the thickness, and numerical discretization. We conclude that if the epithelium is modelled as stroma, the material properties should be reduced by 10\%. While this choice represents a sufficiently good approximation for the simulation of in-vivo mechanical tests, it might result into an underestimation of the postoperative stress in the simulation of refractive surgery.

ABSTRACT. The mechanical properties of the nucleus in eukaryotic cells are vital for protecting genetic information stored in chromatin. The nucleus experiences various mechanical stimuli that can impact chromatin organization and gene expression. Experiments have demonstrated that nuclear deformation can cause temporary or permanent changes in chromatin condensation and activate genes, affecting protein transcription. These changes in chromatin organization can, in turn, alter the mechanical properties of the nucleus, potentially leading to auxetic behavior and a negative Poisson's ratio. We propose a model that represents the mechanical behavior of the nucleus as a chemically-active polymeric gel. In this model, chromatin can exist in two states: heterochromatin, which is self-attracting, and euchromatin, which is repulsive. The model predicts reversible or irreversible changes in chromatin condensation due to external deformation of the nucleus. The model also indicates an auxetic response across a wide range of parameters for both small and large deformations. These findings align with experimental observations and emphasize the crucial role of chromatin organization in the mechanical behavior of the nucleus.

ABSTRACT. Traction Force Microscopy (TFM) integrates experimental and computational methods to study cellular tractions exerted on the extracellular matrix (ECM). The technique involves the measurement of displacements that result from cellular activity occurring in the interior of a certain material that imitates the ECM properties. Traction reconstruction is performed in two main ways: the forward method which, while computationally simple, suffers from important errors due to direct numerical differentiation of noisy displacement data; and the inverse method, which focuses on finding new displacements resembling the measured ones that fulfill specific conditions, offering better traction reconstructions.

The design of inverse methods for traction reconstruction is influenced by several factors, such as nonlinear effects, dimensionality (2D/3D), regularization, among others. Generally, solving the inverse problem involves some kind of matrix inversion, but noise in measured displacements can lead to problematic high maximum values in reconstructed tractions. To address this, Tikhonov regularization is commonly used, penalizing high norm values of computed tractions.

This study aims to compare different inverse methodologies, considering restriction imposition and regularization, to determine which one yields better traction reconstructions. We previously devised the Physics-Based Nonlinear Inverse Method (PBNIM), which enforces nullity of nodal forces at hydrogel nodes without regularization. Here, we implement regularization into PBNIM and develop the Mixed Physics-Based Nonlinear Inverse Method (M-PBNIM), which improves overall traction reconstruction by better estimating maximum tractions at the cell surface. However, regularization introduces the challenge of calibrating the regularization parameter, often done through non-conclusive procedures. Because of this, the non-regularized PBNIM stands out as the most suitable when regularization parameter calibration is omitted, provided that maximum tractions maintain acceptable values with errors comparable to the best inverse approaches. The conclusions emphasize the importance of considering not only traction reconstruction quality but also the efficiency and complexity of implementation when selecting an inverse method.

ABSTRACT. The purely-mechanical model proposed is devoted to explore the interplay between the overall elasticity of the epithelium and the surface tensions associated with its apical/basal sides (for an epithelial sheet/tube). We describe an epithelial monolayer as a thin two-dimensional entity endowed with bulk and surface energy on its apical/basal sides. The interplay between these energetic components characterizes the model: the former favors an undeformed state, while the latter induces bending when there is an imbalance in apical/basal energies. Employing dimension reduction, based on kinematic Ansatz, we simplify the model to a one-dimensional representation of a nonlinear elastic rod. The equilibria of this rod are determined by the competition among the aforementioned energetic contributions. Once the apico-basal tension imbalance overcomes a critical threshold, a subcritical bifurcation appears, leading the epithelium to assume its characteristic folded configuration which is observed in normal conditions. More in details, two dimensionless key parameters, γ and σ (the critical load), are introduced: γ gauges the relative importance of surface energy compared to bulk energy, while σ measures the imbalance between apical and basal tensions. As γ increases, surface energy becomes more influential, causing the shortening of the apical and basal sides and an increase in thickness. A rise in σ promotes curved configurations. Through an asymptotic analysis employing the Lyapunov–Schmidt decomposition method, we discover that the bifurcation is subcritical, a finding corroborated by our branches numerical continuation [1]. Moreover, our model predicts a distinctive mechanical behavior for pre-cancerous cells: cells in the pre-tumoral state exhibit reduced stiffness compared to their healthy counterparts [2]. By using data from Messal et al. (2019), we estimate softening in pre-tumoral pancreatic Neoplasia. These findings are also in accordance with elastographic measures.

References [1] Favata,A., Paroni,R., Recrosi,F. & Tomassetti,G. (2022), IJES, 176, 103677 [2] Favata,A.,Paroni,R.,Recrosi,F. & Tomassetti,G. (2022), Mech.Res.Commun., 124, 103952

ABSTRACT. Cancer progression is characterised by uncontrolled cell growth and changes in the mechanical properties of the extracellular matrix (ECM) of affected tissues [1]. In its avascular stage, tumour growth is strongly influenced by nutrient availability and the physical forces and stresses generated during tissue development. The role of the latter is not yet fully understood and is the subject of intense research, where the development of theoretical and computational models may help to reveal complex cues in growth dynamics [2].

In this work, we consider the tumour (and host) tissue as a porous material and address the interaction between cells, interstitial fluid and ECM through the mechanochemical coupling of cell function. We discuss the numerical solution of the resulting coupled problem and present numerical results illustrating tumour growth under free and constrained conditions.

[1] J.M. Northcott, I.S. Dean, J.K. Mouw, V.M. Weaver (2018). Feeling Stress: The Mechanics of Cancer Progression and Aggresion. Frontiers in Cell and Developmental Biology, Vol. 6:17.

[2] J.A. Bull, H.M. Byrne (2022). The Hallmarks of Mathematical Oncology. Proceedings of the IEEE, Vol. 110, pp. 523-540.

ABSTRACT. Cellular motility emerges after polymerization of actin into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone about the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed departing the well-known theory of Larché-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.

ABSTRACT. Despite the crucial role the agglomeration process plays in both nature and powder technology, the current understanding of the physical mechanisms determining the tensile strength of cohesive agglomerates consisting of fine particles is still limited. Specifically, the quantitative effects of particle shape in conjunction with cohesive-frictional interactions between particles have yet to be fully explained. One straightforward method to examine the influence of particle shape on the strength characteristics of granular materials is by employing hexapod-shaped particles. We used particle dynamics simulations to create agglomerates composed of hexapods and analyzed the effects of aspect ratio and interparticle friction on the force transmission and microstructure such as packing fraction, connectivity and elastic bulk modulus. We also investigate their mechanical behavior under diametral compression to showcase the effect of non-convex particle shape and interlocking on their tensile strength and we analyze the strength and fracture behavior as a function of aspect ratio, friction coefficient, and cohesive force between aggregates for irreversible cohesive interaction. We demonstrate that nonconvex form significantly increases the cohesive strength of the agglomeration for large enough aspect ratios. We show that the ability of thin hexapods to establish contact with their second neighbors and the function of friction in minimizing their disentanglement under diametral compression are connected with this amplifying effect of interlocking on the cohesive strength.

ABSTRACT. Flexible granular chains are linear chains of spherical beads connected by link elements, similar to roller blind chains. These chains form an exciting class of elasto-granular materials, wherein the inclusion of tension-transmitting link elements transforms the mechanical properties of parent cohesionless granular material. These chains exhibit an array of intriguing properties such as jamming at low packing density, strain stiffening, higher stiffness at small coordination numbers etc. Unlike other cohesionless granular materials, which flow and form conical piles on repose, the packings of these chains entangle and form stable vertical standing columns. This flow behaviour makes the study of force transmission and wall pressures in these chain packings an exciting problem to explore. We explore the static pressure distributions in 2D random chain packings and contrast their behaviour with the Janssen effect observed in conventional cohesionless granular materials. Although numerical methods such as Monte Carlo and MD have been employed to study the particle-level mechanics of flexible granular chains. However, most of these studies are carried out for drastically different length scales of molecular polymer melts. In our DEM contact model, the links connecting the beads in the chains are implemented as a combination of linear normal and angular stiffness, which constrains inter-particle elongation and the bending angle between three consecutive beads. We generate 2D chain packings in a vertical cylinder with varying chain length (M), column height, container size and deposition methods. Apart from the wall forces, we evaluate various micro-mechanical, topological and macroscopic parameters to elucidate force chain transmission and deformation of these chain packings. The ability of the chains to form tensile force chains drastically affects the saturation of the column base pressure. Moreover, the flexible geometry of the chains results in the formation of chain loops, leading to larger heterogeneity and anisotropy in contact force chains.

ABSTRACT. By means of particle dynamics simulations, we investigate the orthotropic elastic moduli of dense packings of polyhedral particles with different number of faces. The samples are prepared by isotropic compaction under constant load and zero friction, leading to random close packed configuration of particles with highest density. Then, they were sheared under tri-periodic boundary conditions for different values of interparticle friction coefficient. During shearing, 16 instances corresponding to a wide variety of contact orientation anisotropies were stored and relaxed a static state before applying two distinct strain probes to measure the five independent elastic moduli of the sample. By comparing the simulation data with effective medium theory (EMT), our results clearly show that the elastic moduli are functions of two microstructural parameters: 1) a constraint number that accounts for contact types (face-face and face-edge contacts between polyhedra), and 2) the contact orientation anisotropy. The proposed expression of elastic moduli isolates the direct effect of particle shape, related to the nonaffine particle displacement field from the indirect effect, related to the granular microstructure. The effect of particle shape appears at two levels: on the one hand, through four parameters in the proposed expression, which are independent of friction coefficient, and, on the other hand, through the microstructure reflected by the values of constraint number and fabric anisotropy, which depend on both particle shape and interparticle friction coefficient [1].

ABSTRACT. The simulation of the effective properties of granular media such as diffusion or thermal conductivity is of a great interest for many applications especially for those where experimental measurements are either complex, impossible or expensive to handle.

We developped a simulation tool[1] chaining Discrete Element Method (DEM)[2, 4] and Fast Fourier Transform (FFT)[3] to compute the effective diffusive properties of granular media. The mechanical behaviour and the kinetic of the grains are computed using the Discrete Element Method (DEM). The effective diffusive properties are then computed using the Fast Fourier Transform Method. To make the link between the DEM and the FFT we developped a procedure to voxelize the DEM grains thanks to Merope code[5]. The case of ill defined interface (solid/gas), called fuzzy voxels, is considered carefully and specific treatment is set up. Several treatments are tested and compared and we show that applying a Reuss/Serie model to the fuzzy voxels.

This method is applied to the behaviour of fragmented nuclear fragments to compute its equivalent thermal conductivity. Starting from granulometries characterized experimentally, we set up a two scale procedure to take into account the huge polydispersity characteristic of the fragments. Several thermal effects such as Knudsen and radiation are taken into account and the resulting conductivities are compared with analytical models from the litterature. We evaluate the sensitivity of the two scale scheme and provide experimental validation of the single scale scheme.

REFERENCES [1] T. Calvet, J-M. Vanson and R. Masson, International Journal of Thermal Sciences, 172, 107339, 2022. [2] M. Stasiak, G. Combe, V. Richefeu, G. Armand, J. Zghondi, Computational Particle Mechanics, 9, 825-842, 2022. [3] J-C. Michel, H. Moulinec and P. Suquet, Computer Methods in Applied Mechanics and Engineering, 172, 109-143, 1999. [4] https://richefeu.github.io/rockable/ [5] https://github.com/MarcJos/Merope

ABSTRACT. During a Loss of Coolant Accident (LOCA), fuel rods are heated by the residual power. The resulting increase of internal pressure leads to a ballooning of the cladding which allows the fuel to relocate and, if there is a rupture, to disperse into the primary circuit.

Here, we propose to assimilate the fragmented fuel to a granular medium and implement a Discrete Element Method (DEM) to model the behavior of fragments within the rod. The aim is to describe their relocation through the analysis of packing fraction along the rod. This model echoes previous DEM-focused numerical simulation works on fragment relocation. Some of these models have limitations in terms of representation which we aim to overcome by creating a realistic 3D model to describe the main features of the fuel rod during a LOCA: • The complex shape of the fragments; • The deformation of the cladding and the interaction of fragments with the inner wall; • The interaction of fuel fragments with fission gases and the confinement gas;

The initial developments aimed to adapt the discrete element method and extend it to arbitrary polyhedral geometries, adopting a method based on sphero-polyhedra. This method allows to facilitate the contact detection stage, which is challenging to implement for complex geometries.

Verification and validation test cases of the polyhedral DEM method have been conducted. They serve as benchmarks for applied simulations aimed at studying the effect of size and shape distribution of fragments on relocation in the case of a dry granular medium.

Further developments are in progress to address the effects of fragment interaction with cladding walls and fission gases. Various coupling methods with DEM are being explored, and their selection is the subject of current research efforts.

ABSTRACT. Mechanical nanostructured metamaterials, when used in bulk applications, define a quintessential multiscale problem, with many orders of magnitude in scale separation between the micro and macro domains. Under such conditions, models--computational or otherwise--predicated on the explicit tracking of every individual member of the metamaterial are impractical and uncalled for, since locally large numbers of members deform collectively under applied loading and jointly exhibit well-defined effective behavior that can be characterized as a continuum material law. The identification of such an effective material model is the aim of homogenization theory and discrete-to-continuum techniques. However, mechanical materials fall outside conventional homogenization theory on account of the flexural, or bending, response of their members. We show that modern homogenization theory, based on calculus of variations and notions of Gamma-convergence, can be rigorously extended to account for bending and that the resulting homogenized metamaterials exhibit intrinsic generalized elasticity and retain a characteristic length scale even in the continuum limit. In particular, the homogenized metamaterials are nonlocal, have a built-in size effect and, for members of finite strength, an intrinsic fracture toughness. We illustrate these properties in specific examples including two-dimensional honeycomb and three-dimensional octet metamaterials.

ABSTRACT. Architected materials possess two natural scales : the characteristic size of the microstructure and the size of the macroscopic phenomenons. When the ratio of these scales is small, classical homogenization yields an effective behavior that accurately captures the mechanical response of the material. However, when these materials are submitted to strong variations of the macroscopic fields, non-local effects that can be captured by higher gradient models appear. The asymptotic expansion is a systematic method often used to derive such models in the context of periodic media. However, in the classical asymptotic approaches boundary effects are generally neglected, which is likely to ruin the order of approximation of the solution. Besides, in higher-order models, the order of the equilibrium equations is increased and additional boundary conditions are required. The applicable boundary conditions for strain-gradient models have not yet been clearly identified. To overcome these limitations, we combine an asymptotic-energy-based homogenization scheme with a boundary layer analysis. This procedure results in a set of effective boundary conditions whose order of approximation is consistent with that of the solution to the strain-gradient equilibrium equation. To illustrate our approach, we study a 1D periodic chain of springs. We perform a numerical comparison between the predictions of our matched model and predictions from the full discrete system. We show that our model converges towards the discrete solution at an improved rate compared to the classical homogenization framework. Besides, we solve a long-standing issue related to the non-positivity of strain-gradient stiffnesses. This property has been reported in several papers in the context of asymptotic homogenization but its implications remain unclear. In particular, it is known that such property results in the presence of oscillations in the expression of the homogenized solution. We show on this example that our boundary conditions make these oscillating terms negligible.

ABSTRACT. Formulations based on classical continuum mechanics fail when applied to problems in which scale effects are present due to the discreteness of the matter. In the presented work, different continualization techniques are applied to a 2D beam-grid lattice, thus developing several continuum models that account for the scale effects not captured by the Classic Kirchhoff plate model in dynamic problems. This 2D beam-grid lattice is considered as a reference, and is made up of particles arranged in the x-y plane undergoing displacement in the out-of-plane direction. Adjacent particles are connected by linear rotational springs that are joined to straight segment (bending deformation proportional to their relative rotation). Additionally, each representative unit cell includes springs in the central domain to account for torsion stiffness. Different standard (based on Taylor’s series) and non-standard (employing the pseudo-differential shift operator) continualization procedures are applied to this lattice, the latter leading to new non-classical continuum model with low spatial order, thereby bringing the advantage of not needing extra boundary conditions (unclear physical meaning) to be solved when finite solids are treated. All these models are evaluated via dispersion and natural frequency analyses, comparing their dynamic behaviour with that of the discrete one. Moreover, the intrinsic relationship between wave propagation and vibration of bounded solids is emphasized for both continuum and discrete models. Interestingly, the non-standard models derived in this work are able to accurately capture the scale effects featured by the discrete model through space-time cross derivatives with low spatial order, not presenting any physical inconsistency.

The authors acknowledge support from MCIN/ AEI /10.13039/501100011033 under Grants number PID2021-123294OB-100, from FEDER and ESF. This work has been also supported by the Madrid Government under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M24), and in the context of the V PRICIT.

ABSTRACT. Lattice materials are becoming increasingly important in lightweight design as they can now be manufactured to meet desired properties using advancing additive manufacturing techniques. Among the numerous failure mechanisms that may occur in lattice materials, buckling caused by global compressive loading is of special interest, especially for lattice materials with slender lattice members. Micropolar continuum theory in conjunction with the finite element method is a promising and efficient approach to predict the buckling deformations based on the internal length scale of lattice materials.

Buckling predictions require a geometrically nonlinear model, which is not readily available for micropolar continua.

Therefore, a geometrically nonlinear micropolar continuum model proposed in the literature is implemented in ABAQUS 2019/Standard (Dassault Syst\`emes Simulia Corp., Providence, RI, USA) as a user element, which is verified against benchmark problems. The model is employed for predicting the critical load and the post-buckling behavior of finite-sized lattice beams showing body-centered cubic or primitive cubic base cells. The micropolar elastic constants of the lattice materials required for the constitutive relations are derived using an energy-based homogenization approach commonly used in the literature. The predictions are compared with results obtained using discrete models.

The comparison shows that although the initial stiffnesses of the continuum and discrete models are in good agreement, the buckling loads are overestimated by the micropolar model. However, the postbuckling response is captured well in a qualitative manner even for unstable behavior. This holds true as long as the localized deformations remain small.

ABSTRACT. Metamaterials can present special properties, e.g., negative constitutive parameters and exotic interactions with elastic waves (band gaps, cloaking, focusing, among others), that derive from their underlying microstructures. Thanks to their potential engineering applications, there has been increasing interest in making accurate and computationally cost-effective simulations for metamaterials' design. One approach to account for the complexities of these systems, while remaining less computationally expensive, has been the use of enriched models of the micromorphic type. Although micromorphic-type models have extensively been proven to accurately capture the behavior of infinite-size metamaterials (bulk’s response), their accuracy in capturing the behavior of finite-size metamaterials has been proven to be effective only for sufficiently large metamaterials' specimens.

Working with finite-size metamaterials introduces the need for consistent and appropriate boundary conditions. For example, if we take two bulk samples of an arbitrary metamaterial, they will have the same bulk. However, their boundaries most likely won’t match because the same metamaterial can be cut in different ways. This suggests possible differentiated local boundary effects, which need to be considered when setting the boundary conditions in the homogenized (micromorphic) framework. In this work, we simulate finite-size metamaterials using the reduced relaxed micromorphic model. In order to account for the differentiated response of distinct metamaterial boundaries, we implement a non-coherent interface model with microstructure-driven interface forces. The results of our simulations show that this approach allows for retrieving the differentiated response of finite-size metamaterials that have the same bulk, but distinct boundaries. They also show a possible way to enhance the precision of micromorphic-type metamaterials' simulations when local boundary effects have a significant weight on their response.

ABSTRACT. Our scientific community has made great strides in data-driven design and modeling. However, artificial neural networks are currently developed for specific tasks because they suffer from catastrophic forgetting. This is a major impediment to cooperative data-driven modeling. We present a new method addressing this issue in an attempt to open the field to cooperation.

ABSTRACT. This research introduces a computationally efficient mathematical framework designed to predict the mesoscale (local) strain field in single-phase polycrystalline materials under mechanical loading. The framework utilizes low-rank approximations to estimate the intricate meso-scale strain field precisely, considering the underlying microstructure of single-phase polycrystalline materials. The effectiveness of this framework is evaluated across a broad design space, encompassing various microstructures of single-phase polycrystalline materials and diverse mechanical properties for the constituent phases. Comparative assessments against finite element predictions highlight the predictive capability of the proposed framework. A crucial aspect of this approach involves calibration using data, and the impact of dataset size on accuracy is systematically examined through different statistical measures. Results indicate that the proposed method performs accurately and requires a substantially smaller dataset compared to existing deep learning techniques.

ABSTRACT. This study presents an innovative approach using physics-informed neural operators to create a universal surrogate model. Our focus is on accurately predicting the mechanical behavior of heterogeneous microstructures under a given set of boundary conditions, considering different heterogeneity patterns and phase contrast ratios. We explore different architectures of neural operators and evaluate their effectiveness both with and without the presence of labeled data. A significant achievement of our work is the ability of the network to reliably predict unseen cases, especially in the context of periodic boundary conditions. The model efficiently computes the homogeneous stress tensor, essential for two-scale calculations. We extend our methodology to solve the steady-state heat equation in microstructures with varying conductivity ratios, demonstrating the versatility of our approach. On the one hand, deep neural operators are used, which condense the information of the microstructures through a branch network and evaluate the solution at a given point to the trunk network. On the other hand, a novel integration of operator learning with finite elements is presented. This method solves boundary value problems by minimizing the discretized weak form, exploiting the strengths of the finite element method. We show that the trained neural operator significantly reduces the solution evaluation time compared to traditional methods such as finite element analysis, without compromising accuracy for any arbitrary shape of microstructures. This work opens new avenues for efficient microstructural analysis in materials science.

ABSTRACT. The prediction of the structural response requires the constitutive description of the material from which the structure is built. For complex elastic-plastic anisotropic materials, analytical closed form constitutive models with sufficient accuracy may not exist. Concurrent modeling (i.e. FE^2) is extremely costly, in particular for larger three-dimensional structures.

Alternatively, data driven approaches based on machine learning gains increasing attention. In this contribution such an approach will be presented for a periodic lattice material with cubic material symmetry and elastic-plastic parent material. Not only the elastic anisotropy is very pronounced, but also the initial yield surface and the hardening response is highly direction dependent.

A periodic unit cell model is set up in the framework of the Finite Element Method to predict the non-linear stress response to strain controlled monotonic proportional loading. The resulting data base is used for training, testing, and validation of an artificial neural network. Additionally, energy considerations are included in terms of elastic recoverable and plastic dissipative contributions to distinguish between loading and unloading. Moreover, the predictive capabilities for (mildly) non-proportional strain histories is assessed.

The AI-based constitutive model is implemented as VUMAT into ABAQUS/Explicit to run structural analyses. As example a cantilever beam formed by ten times hundred unit cells is studied under various loading conditions and the performance of the developed constitutive model is evaluated. Since the example beam is small enough to fully discretize the all lattice members, detailed comparison to the reference model is possible.

ABSTRACT. Advancements in computational solid mechanics have accelerated the development of materials, addressing the ongoing need for material optimization with previously un-attainable properties. The genesis of innovative materials and structural systems, such as high entropy alloys and mechanical metamaterials, relies on in-depth knowledge of the underlying physical principles across various scales, while the traditional single-scale modelling methods fail to meet this challenge. And it is still prohibitive to execute multi-scale simulations by cascading full-field single scale maps due to the limitation of computational resources. Developments in data-driven based approaches provide a solution, leveraging the neural network’s ability to process large amounts of data in an accelerated manner and approximate nonlinear maps, which makes it a promising computational tool in solving a variety of challenging physical systems.

In this work, we focus on polycrystalline materials, which are highly important to industry given their broad spectrum of applications. Establishing a precise and trustworthy link between the microstructures of polycrystals and their mechanical behaviours is essential for evaluating their properties and discovering innovative material alternatives. Therefore, building on the latest fundamental progress in AI-based tools, we develop the general micro-mechanics informed neural operator (MINO) for polycrystalline material systems, where the microstructural details are efficiently encoded and passed into the description of macroscopic material response to enable fast multi-scale predictions. In this framework we exploit recent advances in Fourier Neural Operators, which have been shown to be universal estimators for function space mappings. The MINO unlocks the potential for a more profound comprehension of unclear physics and heralds unprecedented opportunities for functionality/feature-lead material design. It promotes a more data-intensive and systematic research paradigm and will eventually enable expedited, property-specific material design with desirable functionalities.

ABSTRACT. Copolymers play an integral role across diverse industries, driven by their abundant availability and adaptable properties. To leverage the vast usage of polymers in industry, there is a crucial need to precisely control the properties of these materials according to specific applications. Polymer characterization has evolved from traditional empirical methods, relying on trial-and-error experimentation, to more advanced strategies. Computational methods, including computer-aided design and simulation, have enabled a systematic exploration of the polymer chemical space, allowing for more precise predictions of properties. In this research endeavor, the primary focus is on comprehensively exploring the properties of copolymer materials, specifically random, block, and alternative copolymers. For reach to this goal, we harness the power of molecular dynamics (MD) sim- ulations. This tool contributed to the calculation of 14 key properties, providing valuable support in our efforts to generate the dataset for 130 copolymer systems with high accuracy. Our study is driven by the overarching goal of addressing a significant gap in reference data for sepcial type of copolymers. These data serve as a valuable foundation for data-driven approach. By combining MD simulations with machine learning (ML) techniques, we aim to develop predictive models for optimizing copolymer performance based on the calculated properties. In addressing this challenge, we aim to provide an in-depth understanding of the molecular composition, configuration, and sequence distribution of copolymers. Our methodology involves utilizing a diverse set of representations, notably a graph-based representation, to achieve this comprehensive understanding. This approach excels in capturing crucial aspects of polymeric materials, encompassing chain architecture, monomer stoichiometry, possible monomer sequences, degree of polymerization, diverse chain topologies, and varying monomer compositions.

ABSTRACT. Glass syntactic polypropylene (GSPP) is used for thermal insulation of subsea pipelines. Flat notched specimens, with two notch root radii, were used to study the mechanisms of deformation and voiding thanks to in-situ tensile tests conducted at Psiché beamline of Soleil Synchrotron Radiation Facility. High resolution data sets (1 px = 1.3 µm) were obtained all along the applied deformation. The interaction between the glass hollow microspheres and the matrix was highlighted using gradually the images of : i) the neat PP matrix; ii) embedded unique microsphere within this matrix; iii) the GSPP composite with the real distribution of microspheres. In the PP-matrix void nucleation, growth and coalescence resulted in crazes like microstructures under the deformed states. For GSPP, voids nucleated at the polar zones, by the decohesion of the matrix, leading to two caps above and below each microsphere. During the deformation of GSPP these voiding mechanisms resulted in a significant irreversible volume change (plastic dilation). This latter was measured: i) at the macroscopic scale, by using the reduction of the width and the thickness; ii) at the microscopic scale, by determining a volume of interest allowing the spatial and time distributions of the void volume fraction to be plotted. Using the mechanics of porous media concepts, Finite Element simulations of the in-situ tests were attempted. The simulated and experimental plastic dilation observed at both macroscopic and microscopic scales were in good agreement.

ABSTRACT. PEEK is a high-performance thermoplastic for demanding load-bearing applications, where reliable prediction of mechanical behavior is essential. As a semi-crystalline polymer, the mechanical performance of PEEK depends on the crystallinity and morphology (including preferential orientation) which depend strongly on cooling and flow conditions during moulding. In injection moulding, variations in processing conditions over the mold induce variations of crystalline morphology and resulting mechanical properties throughout the component. Accurate prediction of the resulting mechanical response requires: 1) prediction of structure development during processing, and 2) an adequate structure-property relation. This study focuses on the latter and aims to develop a micromechanical model that links morphological details such as crystallinity and crystalline orientation distribution directly to mechanical performance.

In the micromechanical approach, the amorphous and crystalline phases are considered separately and connected in aggregates of two-phase layered domains. The response of these domains is coupled via a hybrid interaction law. This model, called the composite inclusion model, has described micro-mechanical relationships in other semi-crystalline materials [1] and is now applied to PEEK. The crystalline phase is modeled with crystal plasticity, governed by crystallographic slip. The amorphous phase is modeled with a phenomenological model, the Eindhoven Glassy Polymer (EGP) model.

To isolate the model parameters for the amorphous phase, PEEK is quenched to a fully amorphous state. Uniaxial compression tests are performed on the amorphous PEEK and modeled using the EGP model. The amorphous phase of the model includes physical aging, for which the effect of temperature- and stress-induced aging is measured in uniaxial tensile tests. The crystalline parameters are then identified by uniaxial compression tests on semi-crystalline material. The model's versatility can be demonstrated by comparing experiments and simulations at different levels of crystallinity and for different thermal histories.

[1] J.A.W. van Dommelen et al., Mechanics Research Communications, 80, 4, 2017

ABSTRACT. Electrospinning is a simple yet robust method for fabricating biomedical fibres by stretching a charged viscoelastic polymer solution using an electric field. During electrospinning, fibres in the micro- to nano-scale range are continuously deposited onto a collecting device leading to an interconnected non-woven mesh. Traditionally, meshes are generated by collecting fibres using plates, drums, bars, discs, and funnels, however these are limited in their ability to scale-up production for commercial applications. In recent years, Mouthuy and collaborators have developed a new automated technique in which fibres are deposited onto a continuous guiding wire to produce electrospun filaments. The filaments can further be processed into braided structures with tailorable mechanical properties, which can be used as scaffold for tissue engineering applications such as tendons and ligaments repair. However, the mechanical and degradation behaviour of this novel biomaterial scaffold has not been characterised.

In this work, we characterise the mechanical properties of electrospun polycaprolactone (PCL) filaments through experimental tests and constitutive modelling. Uniaxial monotonic, cyclic, and stress relaxation tests were conducted, along with (in-situ) SEM characterisation of the porous microstructure. Experimental results reveal that filaments exhibit viscoelastic-viscoplastic behaviour with pronounced post-yield hardening at large deformations, which correlates with the straightening of the fibres at the microscale. Our study also emphasises the role of the testing grips (screw-side or bollard grips) on the apparent material response. A large-deformation viscoelastic-viscoplastic phenomenological model was developed, which can successfully capture the material response up to large strains. Micromechanisms underpinning the macroscopic response are discussed.

ABSTRACT. Polymers are used in many engineering applications due to their high versatility and low-cost production. Adding nano-sized fillers significantly enhances their mechanical performance, yielding polymer nanocomposites suitable for highly demanding applications. These beneficial properties are mainly attributed to the formation of a polymer-filler interphase surrounding the nanoparticles. Within this interphase, the properties of the polymer are altered due to the proximity of the filler particles. Due to the high surface-to-volume ratio of nanofillers, polymer nanocomposites feature a considerable interphase volume fraction. Therefore, precise knowledge of the interphase's mechanical properties is crucial for understanding and modeling the macroscopic material behavior. The small scale makes the interphase region's experimental investigation extremely challenging. Therefore, we rely on molecular dynamics to resolve the microscale and translate the obtained results into constitutive laws. This multiscale approach enables us to identify the inelastic property gradients within the interphase layer and their effect on the macroscopic behavior employing suitable representative volume elements. With these insights, we gain a better mechanical understanding of polymer nanocomposites, a prerequisite to exploiting their full potential.

ABSTRACT. Modelling the mechanical behaviour of heterogeneous materials, such as textile-reinforced polymer composites, requires consideration of the underlying material heterogeneity. For textile composites, this means accounting for the weave architecture in a representative yet computationally efficient manner. Doing this on the mesoscale means including a discrete representation of the weaving pattern of the impregnated textile, along with pure matrix regions as separate entities. A significant challenge is generating high quality finite element discretisations. Traditional meshing techniques often fall short, particularly for proper discretisation of pure matrix regions. The close proximity of complex shaped fibre bundles often creates narrow regions where a high density of elements is required. This poses significant difficulties in generating finite element meshes with an acceptable balance between mesh quality and computational cost.

An attractive alternative is therefore to decouple the geometrical representation from the numerical discretisation, resorting to embedded or immersed methods. In this contribution, we explore the use of the Finite Cell Method [1] to achieve the necessary decoupling. FCM is a popular approach within a class of immersed methods for which straightforward, un-fitted meshes (resembling voxel structures) are used to discretise the unknown fields, while capturing the geometry through specially designed quadrature rules. Thereby, the approach allows the discretisation process to be automated, making it flexible and effective for complex weave architectures. The proposed methodology is demonstrated on several mesoscale structures common to textile-reinforced composites, including both 2D-woven and 3D-woven architectures. In addition, the importance of numerical stabilisation, achievable e.g. through the ghost penalty method, is highlighted and explained. In summary, this contribution shows the benefit and flexibility of FCM in developing mesoscale models of textile composites, to be adopted e.g. in multiscale analyses of larger structures.

[1] E. Rank et al., Computer Methods in Applied Mechanics and Engineering, Vol: 249–252, 2012, pp: 104-115.

ABSTRACT. Coupon testing is pivotal in aeronautical design, offering a great understanding of material behaviour under varied stress conditions. Integrating simulation at this stage could significantly reduce the need for extensive physical tests. This approach reduces costs and time associated with traditional testing, enhancing design optimisation and safety. However, creating any realistic model requires a lot of care and knowledge.

Previous models have demonstrated the ability to predict coupon laminates' strength and damage behaviour, effectively reproducing experimental tests using techniques such as aligned mesh to mitigate mesh-induced direction bias. However, a significant challenge arises with the replication of aligned mesh in complex geometries. While regular mesh is a potential alternative, it could not accurately predict crack propagation. In the case of (±45⁰) plies, the crack prediction in the final failure is captured mainly in only one direction when using regular mesh, whereas, in experimental results, the crack in the specimens appeared in both directions.

A possible method to mitigate this rising issue is defining and using an objective derivative and a rotated frame from the rotation of the fibre rather than using the Abaqus built-in approach (Green-Naghdi stress objectives derivatives).

An initial test of this new method applied to a two-ply laminate, has presented promising results. The preliminary findings suggest that this technique could more accurately predict crack propagation and damage patterns in coupon laminates.

ABSTRACT. Efficient and accurate failure modelling of composite materials is crucial due to their extensive use in the industry. Specifically, simulating translaminar failure, such as Compact Tension (CT) tests using Finite Element analysis has proven to be particularly challenging. This study applies the mesoscale Finite Element Discrete Ply Model (DPM) to the case of unidirectional carbon fibers CT tests. The stacking sequence employed is [45/-45/[0/90]4]s. This configuration has been shown to have significant experimental advantages, such as no specimen buckling and low matrix plasticity. However, it also exhibits a more complex combination of failure modes, including extensive delamination during crack propagation. This leads to inaccurate computation of the strain energy release rate, hence new analysis methods are needed. In the DPM, matrix cracking and delamination are explicitly represented. Failure modes such as fiber failure in tension/compression, shear damage and crushing are modelled within the behavior volume elements. A new law that accounts for the increase in compressive failure strain when planar or out-of-plane strain gradients are present, is proposed and shown to be essential to the correct complete computation of the failure scenario. This approach shows relevant numerical and experimental correlation, both for the force-displacement curves and for the strain energy release rate GIC computed with the compliance method. To address the issue of the complex CT failure scenario, the model estimates the energy dissipated by each failure mode (namely delamination, matrix cracking and fiber failure). A numerical R-curve is also computed directly from these energies, allowing the discussion of the different ways of computing R-curves, numerically and experimentally. Eventually, the R-curve effect (i.e. an increase in GIC with the crack length) is shown to be related to the damage zone height, demonstrating that this effect is indeed not material but structural.

ABSTRACT. Numerical simulation is a promising method to evaluate risk associated to an accidental loading on a structure in service, but a numerically efficient evaluation remains difficult due to the nature of the loadings to be accounted for. Accidental events are usually transient dynamic events modelled with explicit finite element code. To accurately predict damage and strength, this loading must be added up to the current structure loads. Indeed, structures are generally stressed when an accidental event occurs, initial loads are usually quasi-static and are efficiently solved using implicit-based finite element code. An existing strategy in commercial finite element code to introduce an initial loading consists in using a viscous dynamic relaxation, but the associated cost may become tremendous: an important number of increment is necessary for the damping to dissipate the kinetic energy and the time increment must remain lower than the critical time step. This presentation aims at proposing an efficient and non-intrusive methodology to take into account initial in-service loads for the evaluation of transient dynamic loadings, by an alternate use of implicit and explicit solver. Efficiency will be demonstrated with a residual thermal stress simulation of composite materials, induced by the manufacturing process and influencing damage initiation. To our best knowledge, this pre-stress has never been accounted for in transient simulation using an explicit solver, such as impact, despite a wide literature about this topic. In a second time we will extend the methodology to compression after impact, and an impact simulation will be conducted on a stiffened panel initially subjected to a tensile load. Indeed, this component is representative of a fuselage part in the aeronautical industry. In conclusion, limits of the strategy and potential future developments will be exposed.

ABSTRACT. The advancement of lattice materials has recently gained significant traction through the application of reduced-scale additive manufacturing techniques. These fabrication methods enable precise manipulation of geometrical features at both the micro and nanoscales, offering control over macroscopic properties and facilitating the production of lattices with exceptional mechanical characteristics. Architected materials, characterized by heightened stiffness and an impressive strength-to-weight ratio, have found widespread utility in high-strength lightweight materials, energy storage applications, and various other fields. While conventional periodic lattices typically rely on unit cells featuring struts with uniform cross-sections, a strategic redistribution of material along the strut length holds promise for enhancing the material's mechanical response, particularly in bending-dominated topologies [1].

In this investigation, we scrutinize 2D periodic lattices, bending and stretch dominated, aiming to quantify the impact of solid distribution on their mechanical properties. Employing a combination of analytical calculations, finite element modelling, and Genetic Algorithm techniques, we conduct multi-objective optimization of the strut shape to maximize stiffness, yield, and buckling strength. Multiple strategies of redistributing the material along the strut are assessed while benchmarking against the regular-shaped lattices. The unit cell is subjected to diverse loading conditions, and we assess how relative density and material redistribution influence the location of plastic hinge formation and the transition between plastic failure and buckling. Periodic lattices with optimized topologies are fabricated at finite sizes and subjected to experimental testing to validate the predictions of the theoretical models.

REFERENCES [1] Simone AE, Gibson LJ. Effects of solid distribution on the stiffness and strength of metallic foams. Acta Materialia 1998; 46: 2139-50.

ABSTRACT. Most of the natural structures such as bone and tendons, which have been an influential source of inspiration for hierarchical materials design do not have grain structures similar to those that are seen in crystalline metals. Therefore, designing bio-inspired metallic materials with a hierarchical structure such as additively manufactured lattice structures (AMLS) lack from benefiting the property of grain structures. This presentation demonstrates that simultaneously considering the effects of topology and microstructure on the mechanical behavior of AMLS has the potential to substantially improve key performance metrics, e.g., energy dissipation, and to avoid widely reported drastic strength drop of AMLS at the onset of yielding instead, an ever-hardening response is achieved. The distinguishing feature of our approach is that the topological optimization is performed while accounting for the heterogeneous distribution of strut-level microstructural features and concomitant mechanical behavior, which leads to new insights relative to peak AMLS structural performance. A new set of new topologies are designed, built, and validated against experiments. The new topologies demonstrate over 50% improvement on average in energy absorption capacity and flow stress, respectively, of topologies that had been previously optimized using a homogeneous constitutive model throughout the unit cell.

ABSTRACT. By tailoring their microstructural features, microstructured materials can exhibit widely tunable effective properties that are unreachable or even beyond those of the base materials, such as negative Poisson's ratio and negative thermal expansion coefficient. Strut-based lattice structures are typical examples. If more than one base material is introduced in a lattice structure, its effective properties rely on the base material properties as well. To this end, a much wider design space is attained. In practice, the design and application of microstructured materials are two-fold tasks: forward prediction and inverse design. The former tackles the prediction of effective properties of a specified microstructure. The latter is aimed at designing a microstructure with specified target effective properties.

In this contribution, we introduce a few novel bimaterial strut-based lattice structures. They can exhibit negative Poisson's ratios and/or negative thermal expansion coefficients. We consider their inverse design by a data-driven method. We exploit the computational homogenization method to evaluate the effective thermoelastic properties of numerous structure designs with varying structural features, which results in a dataset consisting of structural features paired with the corresponding effective properties. For each type of lattice structure, we construct two artificial neural network (ANN) surrogate models for the forward prediction and inverse design. The ANN models are trained and verified with the dataset. Subsequently, the performance of these data-driven surrogate models is illustrated by typical forward and inverse design tasks. These ANN models will facilitate the application of these novel bimaterial lattice structures in different engineering scenarios for structural and/or functional purposes.

ABSTRACT. Laser-based powder bed fusion (LPBF) represents a highly versatile additive manufacturing method widely used for processing metals. Despite extensive research spanning several decades in this active scientific domain, numerous unanswered questions persist regarding the intricate interplay between process parameters and microstructural transformations. To enhance our comprehension of this relationship, we have developed two compact LPBF devices compatible with various synchrotron and neutron X-ray diffraction and imaging beamlines, enabling in situ investigations.

These setups enable the real-time monitoring of crystallographic phases, cracks, pores, and other phenomena during LPBF. They are capable of examining small samples with microsecond-scale time resolution or larger centimeter-sized samples with time resolutions spanning seconds to minutes. In this presentation, we highlight recent progress and outcomes from both setups. Specifically, we demonstrate the effectiveness of operando X-ray diffraction in tracing phase evolution, local cooling rates, and recrystallization. Additionally, our fast in situ X-ray radiography provides insights into cracking mechanisms and the kinetics of multi-material mixing. Integration with acoustic and optical sensors enhances these experiments, supplying essential input for machine-learning algorithms.

Furthermore, we explore the application of neutrons for in situ strain characterization through neutron diffraction and Bragg edge imaging, defect visualization via neutron dark-field imaging, and determination of magnetic phase fraction utilizing polarization contrast neutron imaging. Our findings contribute significantly to advancing our understanding of the LPBF process, offering valuable insights for informed decision-making and continuous improvement in additive manufacturing practices.

ABSTRACT. Direct Energy Deposition (DED) technologies have undergone extensive research and investigation, finding applications across various industries such as medical, automotive, aerospace, tooling, and remanufacturing. Despite their versatile applications, ensuring the quality and repeatability of DED parts remains challenging due to the complex physical phenomena during production. In-situ temperature monitoring during DED plays a pivotal role in understanding process-property relationships and optimizing the process.

Adapted monitoring techniques were employed to analyze thermal behavior in solid and liquid states during the DED process of a low-carbon steel. A spatially and temporally resolved temperature measurement tool based on a commercial high-speed camera using a 2D mono-band technique was used to measure melt pool temperature, while an infrared camera was employed to measure temperature in solid zones. The application of these methodologies helped enhancing the understanding of the interconnections between process parameters, observed thermal phenomena, and part characteristics to achieve the desired build quality and microstructures.

Selective results will be presented to show the relationships between process parameters, melt pool geometry and temperatures. Moreover, the developed methodology allows a complete monitoring of local thermal history, and a metallurgical characterization has been performed to link the thermal history with the final microstructure. Such relationships is particularly important for low-carbon steel as the microstructure could evolve under the effect of tempering.

In conclusion, the in-situ temperature methodologies serve as insightful tools for selecting optimal process parameters and ensuring the desired properties of DED components.

ABSTRACT. The aim of this study is to investigate the potential of in-process laser heat treatment during additive manufacturing of Ti-6Al-4V in order to control the quantities of α'/α and β phases during building. The eventual goal is to study the potential of such in process laser treatments to replace costly and time-consuming post building heat treatments.

Operando synchrotron X-ray diffraction was carried out at the ID31 beamline of the European Synchrotron Radiation Facility (ESRF, France) during laser metal deposition (LMD) of Ti6Al4V using a miniature LMD machine [1]; in order to monitor the evolution of phases and their quantities during the printing process and during laser heat treatments steps.

Scanning electron microscopy was used to analyse the microstructures of non-heat-treated and heat-treated samples in order to obtain information on the different effects of such heat treatments i.e. phase morphologies and to differentiate between the α’ and α phase content.

This study aims to provide insight into the phase transformations that occur during printing, as well as the evolution of phase fractions as a function of time and the number of added layers. Additionally, the study aims to give understanding into the effect of such in process heat treatments on the quantity and morphology of the phases.

[1] S. Gaudez, K. A. Abdesselam, H. Gharbi, Z. Hegedüs, U. Lienert, W. Pantleon and M. V. Upadhyay, High-resolution reciprocal space mapping reveals dislocation structure evolution during 3D printing, Additive Manufacturing, Volume 71, 2023. DOI: https://doi.org/10.1016/j.addma.2023.103602

ABSTRACT. Laser powder bed fusion (PBF-LB/M) has long been a subject of interest due to the possibilities it offers in terms of design flexibility, enabling the fabrication of geometries not achievable otherwise. This is of special interest regarding the manufacture of thin-wall sections (<1 mm) for cooling channels, heat exchangers, or lattice structures, amongst other applications. Additive manufacturing of thin sections can be particularly challenging due to different phenomena such as heat accumulation, geometrical accuracy, or residual stress distribution. Therefore, further efforts are needed to gain a deep understanding of the relationship between the processing parameters and, more specifically, the scanning strategy, and the resulting microstructure, as this would contribute to enhance thin wall performance. This study investigates the influence of pre- and post-contour scanning on the microstructure of thin-wall Inconel 939 (IN939) structures produced by laser powder bed fusion (PBF-LB/M) [1]. Optical and scanning electron microscopy techniques, including electron backscattered diffraction (EBSD), are used to characterize the microstructure of the manufactured thin sections at different length scales. The influence of the scanning order and of the wall thickness on different microstructural features is discussed in depth. Our findings reveal that pre-contouring mitigates heat accumulation issues, reducing grain and melt pool size and the density of geometrically necessary dislocations (GNDs). This strategy effectively shifts normalized enthalpy towards lower values, thereby enhancing processability for thin sections. Overall, this study demonstrates the potential of pre-contouring as an effective method to improve printability of thin-wall sections. [1] I. Rodríguez-Barber, A. M. Fernández-Blanco, I. Unanue-Arruti, I. Madariaga-Rodríguez, S. Milenkovic, and M. T. Pérez-Prado, “Laser powder bed fusion of the Ni superalloy Inconel 939 using pulsed wave emission,” Mater. Sci. Eng. A, vol. 870, no. February, 2023, doi: 10.1016/j.msea.2023.144864.

ABSTRACT. Shape memory alloys (SMA) offer unique shape memory (SME) or superelastic (SE) effects that have attracted the interest of different industrial sectors, such as aerospace, automotive, robotics, and biomedical devices. NiTi, also called nitinol, is the most extensively used SMA in the biomedical field due to its excellent biocompatibility, corrosion resistance and mechanical properties, especially in manufacturing self-expandable cardiovascular devices. However, current methods for manufacturing NiTi-based cardiovascular devices only allow for simple geometries and prevent the manufacturing of patient-specific personalized devices. In recent years, laser powder bed fusion (LPBF) has emerged as an additive manufacturing technique that should allow both the production of complex-shaped and custom-made NiTi devices. In order to manufacture different devices for cardiovascular applications, two types of NiTi composition have been used to achieve the two properties of superelasticity and shape memory. To do this, the process parameters were optimized to obtain the maximum density of the part and draw a graph where the optimal printing area can be observed. These process parameters were employed for the manufacture of cardiovascular devices. The design of different stent models has been tested in axial and radial compression to evaluate how it influences their mechanical properties.

ABSTRACT. Human cortical bone undergoes remodeling processes resulting in a hierarchical, heterogeneous, anisotropic microstructure. Osteons (~200-micrometer diameter) are a key feature, introducing a microstructure length scale. The cortical wall thickness (~5 millimeters) is the structural dimension. Crack tip fields are therefore disturbed by the microstructure. Currently, measurements of fracture toughness of bone use either linear elastic fracture mechanics or the J-integral. This neglects the length scale dependence of fracture properties emerging from the competing length scales. Here, quasi-brittle fracture mechanics is used which introduces a length scale.

Human cadaveric femur tissue is sectioned into nominal 4 x 4 x 24 mm3 beams and notched endostally at half height. Low-rate, in-situ 4-point bending experiments are undertaken in a 3D X-ray microscope with a bath of saline to maintain tissue hydration. At peak load, the specimen is held in the deformed configuration while a 3D image of the sample is obtained (voxel size ~4.2 microns). The size of the fracture process zone (FPZ) is then measured directly from 3D images. The effective crack length (sum of initial notch and FPZ size) is used to compute the quasi-brittle fracture toughness. Experiments reveal the FPZ size in human cortical bone in the transverse direction is 600 to 1000 micrometers, i.e. extending across 3-5 osteons. Using standard ASTM configuration factors and accounting for the FPZ size results in quasi-brittle fracture toughness in the range of Gc=1-2 N/mm, which is approximately 70% larger than that determined from LEFM. When microstructure heterogeneity and anisotropy are considered and evaluated computationally for specimen-specific configurations, Gc is double that obtained with the ASTM configuration. We conclude by discussing the potential implications of using quasi-brittle fracture mechanics to interpret the effects of aging and therapeutics on osteoporosis.

This work is supported by NSF (CMMI) award 1952993. G.G. is supported by NSF-GRF DGE-1842166.

ABSTRACT. Fracture is an irreversible process in brittle materials, and one modeling method that has become increasingly popular in science in recent years is the phase-field fracture method. Here, a discrete crack is approximated by a smeared field variable, the phase-field. Several strategies have been proposed to maintain the irreversibility condition. Bourdin et al. used a direct method to handle the irreversibility by introducing a threshold value to fix the fully damaged degrees of freedom. A penalization method was proposed by Gerasimov and De Lorenzis, which includes an additional penalty term in the phase-field evolution equations. Miehe et al. introduced a history field as the crack driving force related quantity, which is the maximum of all tensile strain energies over the simulation time. Based on the definition of the history field, there are two possible options. If the history field is defined only as the maximum of all previous load steps, the coupling of the displacement and phase-field equations is only one way and allows solving a load step in a single staggered iteration. However, small pseudo time-step sizes are essential for proper fracture detection. On the other hand, multiple staggered iterations are required when the history variable depends on the tensile strain energies of the current load step, but this allows the number of load steps to be significantly reduced. From a performance perspective, the multiple staggered iterations lead to computationally expensive simulations. We have combined different methods to reduce the computational cost while still achieving physically correct results. In addition to adaptivity in space, an improved energy-based convergence criterion is introduced for the combined convergence control in the staggered iterations, and adaptivity in time is integrated. We determine appropriate modeling parameters in typical benchmark simulations and apply them to more complex and realistic simulations of a pre-cracked particle-reinforced microstructure.

ABSTRACT. The pursuit of high-performance energy storage devices demands a comprehensive understanding of the intricate interplay between chemical and mechanical phenomena, and the damage and failure mechanisms within electrode materials. In this work we proposed a length-scale insensitive cohesive chemo-mechanical phase-field model for simulating and elucidating fracture-induced damage and degradation phenomena in the polycrystalline LixNi0.5Mn0.3Co0.2O2 (NMC532) cathode. One significant challenge thereby is how a diffusive interface-based phase-field fracture model can reproduce the sharp interfacial damage at grain boundary/interface, while preserving the energy-based fracture criterion (global dissipation equivalence). In particular, the length scale insensitivity of the proposed phase-field model in the context of inter- and trans-(intra-) granular fractures is validated with several representative benchmark examples. As application examples, the (de-)lithiation induced fracture and degradation in the polycrystalline NMC532 cathode materials was simulated. Thereby image-based reconstructed 3D polycrystalline geometry was employed for finite element (FE) mesh. Simulation results show that the model can capture various crack evolution features (e.g., nucleation, propagation, branching and diverse modes including inter-/trans-(intra-) granular patterns. Specifically, we reveal the impact of various microstructure aspects, including grain boundary fracture energy, charging rates, grain size. This comprehensive analysis provides valuable insights into the chemo-mechanical fracture and degradation within polycrystalline NMC cathodes.

ABSTRACT. Refractories are polycrystalline, porous, heterogeneous, non-metallic materials utilized as protective liners in high-temperature manufacturing processes. Microscopic and mechanical characterization studies of MgO-C refractories in the literature show a strong correlation between the underlying microstructure and the thermo-mechanical response of these materials. The present study focuses on developing a simulation tool that assesses the behavior of recycled refractory composites, specifically the influence of microstructural features on their thermal shock resistance. Experimental findings show that the anisotropic behavior of graphite flakes and their preferred orientation significantly influence the mechanical properties of MgO-C refractories. In contrast to prior modeling methodologies, the heterogeneous microstructure of MgO-C in this approach is conceptualized as a three-phase composite by explicitly modeling the graphite phase along with coarse magnesia aggregates and a homogenized matrix. A pre-processing tool is developed to synthetically generate this idealized 2D microstructure representation from statistical data, utilizing open-access Python packages [1]. According to the current hypothesis and experimental findings, the principal mechanism of damage in these materials involves the debonding of phase interfaces due to thermally-induced stresses. Consequently, this interface damage is modeled using the cohesive zone approach [2]. Basic thermal shock simulations are performed employing the synthetic microstructures to investigate the influences of thermal expansion coefficient mismatches and thermal gradients on the local interface damage. Furthermore, a sensitivity study is presented to analyze the influence of the graphite flake orientation and volume fraction on the thermal shock resistance of these refractory composite materials.

[1] K. A. Hart and J. J. Rimoli. Generation of statistically representative microstructures with direct grain geometry control. Computer Methods in Applied Mechanics and Engineering, 370, 2020.

[2] M. Kuna and S. Roth. General remarks on cyclic cohesive zone models. International Journal of Fracture, 196, 11 2015.

ABSTRACT. In fracture mechanics, the study of crack propagation in pre-cracked specimens with numerical simulations presents an unstable propagation with load and displacement control in many cases. In the case of the Phase Field Fracture model, the instability prevents the use of monolithic algorithms due to the non-convexity of the functional that needs to be minimized, forcing the use of stagger schemes that may require several hundred iterations to reach a stable configuration [1]. This problem is even greater when studying crack propagation through the microstructure in micromechanical problems. In this work, an energy dissipation control method [2] based on the crack length (CLCS) has been developed for Phase Field Fracture model to control the applied external load by imposing a monotonic crack growth. This technique allows the use of monolithic algorithms and the control allows to obtain the required stress/strain decrease path (snap-back behavior) corresponding to stable crack propagation. The technique has been implemented in a FFT based resolution framework [3] with a much higher computational efficiency in periodic micromechanical problems. The control technique is validated with a FEM based framework with CLCS in problems with analytical solution. The accuracy and efficiency of both proposed frameworks is studied. Finally, the resolution of multiple crack propagation in 2D and 3D microstructures of composite materials is presented.

REFERENCES [1] T. Gerasimov, L. De Lorenzis. A line search assisted monolithic approach for phase-field computing of brittle fracture. Computer Methods in Applied Mechanics and Engineering, 312:276–303, 2016. [2] Carpinteri A, Accornero F. Multiple snap-back instabilities in progressive microcracking coalescence. Engineering Fracture Mechanics, 187:272–281, 2018. [3] S. Lucarini, M. Upadyhay, J. Segurado, FFT based approaches in micromechanics: fundamentals, methods and applications. Modelling and Simulation in Materials Science and Engineering 30 023002, 2022.

ABSTRACT. The talk addresses two fundamental questions related by the effect of the third stress invariant in ductile failure: (i) What is the rationale for this effect? (ii) Are shearing states always “less ductile” than axisymmetric ones? To this end, the theory of unhomogeneous yielding is presented based on the concept of percolation of elastically unloaded domains through a network of pores. The concept is illustrated through standard single-void unit cells as well as many-void cells. It is shown that the concept of unhomogeneous yielding suffices to explain all known traits of J3 dependent failure, as gleaned from micromechanical simulations as well as available experiments. The theory also suggests that question (ii) may be answered with a negative depending on initial states. To further examine that, micromechanical voided cell calculations are carried out. The unit cell is subjected to proportional loading and fully periodic boundary conditions. The progression of elastic unloading in the unit cell is analyzed, leading to a precise detection of unhomogeneous yielding. Overall strain localization is determined by evaluating ``on the fly'' the tangent operator using a perturbation method. The connection between unhomogeneous yielding and strain localization is thus thoroughly investigated. Other critical strain measures used in the recent literature are monitored and their relevance to failure by void coalescence or strain localization is discussed. Our findings have far reaching implications since all available theories, of the critical strain type or Gurson-enhanced, assume a positive answer to question (ii). The effects of initial porosity and strain hardening in modulating the relative ductility under tension versus shear are further examined.

ABSTRACT. Industrial power generation and transport structures, designed for a typical service life of up to 40 years, require a profound understanding of the long-term evolution of material behavior to ensure the safety and reliability of these installations. Small coupons (2–3 mm thickness) extracted from these structures may provide material for machining sub-size test specimens, enabling the characterization of aged materials. Conducting tests on these mini-specimens allows quasi-non-destructive sampling, avoiding disruptions to transit or subsequent repairs.

The test campaign comprises small tensile and fracture mechanics specimens, including Compact Tensile (CT) specimens. However, due to their reduced size, mini-CT specimens do not meet the validity criteria of the ASTM E1820 standard. Therefore, this study proposes to use the finite element method to simulate valid CT specimens using a nonlocal Gurson-Tvergaard-Needleman (GTN) model with parameters tuned for sub-size specimens.

Focusing on two ferrite-pearlite steels - a vintage steel used for pipe manufacturing and a modern steel for tube production - this study covers tests conducted on both standard and sub-size CT specimens with thicknesses of 2, 3, and 5 mm. The study involves the derivation of J-R curves for crack propagation resistance using the load/unload compliance technique, yielding highly reproducible results. Particularly for the vintage steel, toughness decreases with thickness, whereas for the modern steel it increases.

The mechanical tests are additionally and comprehensively simulated using the finite element method and a nonlocal GTN model, which captures both plasticity and ductile damage. Model parameters, including hardening, damage (void nucleation and growth), and internal lengths, are fitted for both materials. The choice of employing a nonlocal formulation specifically ensures mesh independence. The model can be effectively used to simulate specimens large enough to meet the validity criteria of the ASTM E1820 standard, and the resulting J-R curve can be used for safety evaluation.

ABSTRACT. Thin-walled structures find widespread applications across various fields, such as in automotive and aerospace. Achieving optimal weight reduction is crucial, requiring thin structures while preserving the best combination of ductility, strength, and resistance to crack propagation through a high fracture toughness (FT), e.g. [1]. The literature shows that there exists an optimum thickness, typically in the mm range at which FT exhibits a maximum. Although this has been known for five decades, very few studies attempted at understanding and predicting this optimum FT. In this context, 3D finite element simulations are performed using a so-called small-scale yielding (SSY) model. A SSY model considers a cylindrical region with a very large external radius with a through-thickness crack with the tip located at the center region. Monotonically increasing displacements are applied at the outer periphery following the elastic mode I solution, corresponding to a well-defined applied K_I value. In this work, we present the results of a parameter study, relying on the nonlocal advanced Gurson model by Nguyen et al. [2]. This model has been validated against direct experimental data, recently demonstrating its capacity to, among others, capture thickness effects in the case of a flat crack propagation mode. The goal is to explore the effects of plate thickness, hardening law, and damage parameters on FT and in particular, on the FT thickness dependence. In particular, the focus is on the peak FT and the corresponding thickness, and how these are affected by the material parameters.

REFERENCES [1] 10.1016/j.actamat.2023.119280 [2] 10.1016/j.jmps.2020.103891

ABSTRACT. Steel sheets are extensively used in the automotive industry for an excellent combination of strength-ductility-cost performances. However, the ongoing optimization of this set of usually conflicting properties has brought forward cracking resistance issues in new advanced high strength steel products, leading to fracture toughness concerns.

This study investigates an unusual alternating failure mode transition from ductile damage to brittle (quasi-)cleavage, leading to arrowhead marking (AHM) patterns pointing towards the crack propagation direction. The sheet materials are 1.5 mm thick medium-manganese and quenching & partitioning steel grades. Arcan cracking tests have been carried out, involving the propagation of cracks into modified single edge notched tensile specimens where the initial notch can be tilted with respect to the tensile direction. One of the goals is to discriminate the influence of shear stress at fixed stress triaxiality on crack initiation and propagation. Two loading angles, 0° (pure mode I) and 45° (mixed mode I & II) were imposed, as well as three loading speeds, 0.1, 1.0 and 10 mm/min.

All materials and loading conditions lead to a slant mode exhibiting well-defined arrowhead markings on the fracture surfaces. The phenomenon is strain rate sensitive as the number of AHMs directly increases with loading rate while the AHMs size and spacing both decrease. Further geometrical characterization of these arrowhead markings suggests a strong connection between the intrinsic energies of both ductile and brittle failure modes. The mechanism presumably involves a crack arrest and re-blunting process. The understanding and mitigation of this singular failure mechanism is of prime importance in the context of the development of high performance steel sheets.

ABSTRACT. In the case of aluminium structures, welding may introduce weak zones, so-called heat-affected zones (HAZ), close to the weld. Such zones should be accounted for when predicting the overall behaviour of the structure since the deformation tends to localise within such weak zones, leading to failure initiation. In an early design stage, the structural capacity is usually assessed based on numerical simulations using the finite-element (FE) method and shell elements rather than carrying out extensive test campaigns. A literature review reveals that numerical tools could predict the spatial variation of material properties within a HAZ when using a fine discretisation of solid elements. No unified approach, however, exists for large-scale analyses of thin-walled structures where only a few shell elements represent the HAZ behaviour until fracture.

To address this challenge, this work presents a virtual calibration procedure establishing the mechanical behaviour of a welded aluminium connection relevant to an early design stage. A modelling framework that captures the overall weld and HAZ behaviour until fracture in large-scale analyses is calibrated using a multi-scale approach. The input is the chemical composition and the through-process history of the material, where welding simulations are used to account for the welding process. A nanostructure model predicts the material flow stress by considering the intrinsic resistance to dislocation motion and classical dislocation theory. The spatial variation of flow stress is introduced into a detailed FE model of an idealised HAZ, and the plasticity and fracture parameters for the shell elements are based on this HAZ. To this end, numerical simulations using the proposed calibration procedure are compared against experiments.

ABSTRACT. Phase-transforming solids are a distinct class of multifunctional materials renowned for their remarkable thermomechanical properties. These materials undergo microstructure evolution during specific stress- and temperature-induced phase transformations involving transitions between austenite and multi-variant martensite. The resulting hysteretic behavior, mainly characterized by energy dissipation, is crucial for understanding their performance. Experimental data suggests that phase-transforming solids exhibit rate-independent behavior under quasi-static loading conditions, implying that hysteresis loops retain a finite width even at extremely slow loading rates. The phase-field method has emerged as a powerful tool for modeling these intricate interface dynamics, with remarkable capabilities to capture complex interface topologies’ evolution accurately. Despite significant advancements in this field, see [1] and the references therein, notable gaps still exist in our understanding of these complex phenomena. Especially since most existing models often employ rate-dependent dissipation formulations, thus limiting their ability to replicate thermo-elastic hysteresis loops under quasi-static loading conditions. To address these limitations, this study builds upon a recently proposed thermomechanically coupled and variationally consistent phase-field approach that seamlessly integrates both rate-dependent and rate-independent driving force formulations, as detailed in [2]. Finite element simulations demonstrate the practical applicability of this approach, exploring microstructure formation in twinned martensite in shape memory alloy systems. The analysis includes rate-dependent and -independent stress- and temperature-induced hysteresis loops, the influence of driving force threshold values, and calibration of system parameters with experimentally observed martensite temperatures. This comprehensive modeling framework enhances our understanding and predictive capabilities for the thermo-elastic behavior of these unique materials, facilitating their efficient utilization in engineering applications.

References: [1] L. Xu, T. Baxevanis, D. C. Lagoudas, 2019, Smart Mater. Struct. 28(7), 074004. [2] O. El Khatib, V. von Oertzen, S. A. Patil, B. Kiefer, 2022, Proc. Appl. Math. Mech. 23(2), e202300273.

ABSTRACT. We present a modified Newton scheme applied to a thermomechanical shape memory alloy model, which improves the convergence. Key feature of the model, which is a modified version of the model by Sedlák et al. 2012, is its capability to accurately model the shape memory effect, as well as the superelastic behavior by a thermomechanical potential, compare with Sielenkämper & Wulfinghoff 2022. The variation of this potential yields the energy balance, the linear momentum balance and the evolution equations of the internal variables. Yield and transformation criteria are derived form the corresponding dual dissipation potential. In order to improve the convergence of the thermomechanical model the Newton scheme is adapted using a line search approach. Therefore, the residuum of the convex thermomechanical potential is linearized. The step size of each Newton step is adapted such that the local minimum of each step is approximated as starting point for the following Newton step. This approach improves the numerical robustness of the Newton scheme.

ABSTRACT. Metals under extreme conditions (high stress, high temperature, high flux of radiations, etc.) exhibit extended defects such as dislocations and cavities whose interactions and evolution dictate the macroscopic response of the whole material. However, because of their multi-physics aspects, the underlying phenomena are difficult to characterize, either by numerical simulations or by experimental approaches. Therefore, there is a need to develop efficient and physically justified numerical tools that are able to tackle such problems.

In this work, we propose a phase-field model that couples vacancy diffusion, dislocation climb and pore evolution [1]. This model naturally accounts for the elastic interactions between the objects and guarantees through variational constraints that matter is conserved when vacancies are exchanged [2].

In a first part, we will present the model and provide some details about its numerical implementation that include an improved solver for the equation controlling the vacancy field evolution. We will show that the use of this solver drastically increases the accessible diffusion time scale, allowing us to perform efficient mesoscopic simulations. In a second part, we will validate the phase-field model by comparing numerical results of elementary systems with known analytical results. In a third and last part, we will present results from 2D-simulations of climbing dislocations interacting with an assembly of cavities, highlighting a significant role of elastic interactions on the microstructural evolution of irradiated materials.

References [1] B. Dabas. PhD Thesis of Sorbonne University, 2022. [2] P. A. Geslin, B. Appolaire, A. Finel. Applied Physics Letters, 2014, 104(1), 011903.

ABSTRACT. High-entropy alloys (HEAs) exhibit great promise for engineering application due to their superior mechanical property combinations. Intrinsic chemical disorder and the subsequent interfacial roughening have posed formidable challenges in elucidating the grain boundary (GB)-mediated plasticity in HEAs. Here using a self-propelling atomistic algorithm – activation relaxation technique (ART) – to probe the complex energy landscape of the CoCrFeMnNi HEAs, in conjunction with location-specific perturbations across GBs exposed to different environments, we investigate atomic-reconfiguration ensembles near GBs and their sensitivities to various chemo-mechanical conditions. Two distinct modes, collective and random, are discovered and decomposed. Their partitions are dictated by multiple factors, including the activation energy window, external mechanical loading, and local compositions at GBs. Remarkably, Fe has a disproportionately promoting effect on collective events which is immediately related to slip activities, and Fe enrichment at GB amplifies such positive effect. In stark contrast, Cr atoms suppress the emission of partial dislocations from GBs. These findings imply promising solutions – via synergistic combination of microalloying, heat treatment, and mechanical loading – to selectively trigger desired plasticity modes at needed deformation stage, and hence to achieve an enhanced tunability of HEAs' mechanical behaviors.

ABSTRACT. Wide-range applications of high entropy materials (HEA) requires their superior mechanical properties, which essentially relies on grain boundary (GB) stability for sustaining plastic deformation. While the fundamental mechanisms of GB migration in HEA differ from the ones in conventional materials due to lattice distortion and local chemical environments. Particularly the GB segregation in HEA always accompanies local chemical order (LCO) change. To quantificationally and efficiently investigate the impacts of solute segregation and chemical order on GB migration, we applied atomistic simulations for the NbMoTaW multiprincipal element alloy. Assisted by a contrived Nb-rich model, it is found that solute segregation and chemical order synergistically inhibit GB migration. Nb segregation increase the critical stress for GB migration, and the presence of chemical order further enhances the resistance of GB to plastic deformation. The destruction of local ordering structures is responsible for the difficult GB migration. Transition pathway analyses show that GB modified with both Nb segregation and chemical order requires high migration barrier, and the prior migration of GB sites tends to avoid regions with heavier chemical order. These results provide new insight into how chemical complexity affects elementary GB motion and contribute to manipulating the stability of MPEAs.

ABSTRACT. Consequences of head injuries are not limited to the victim alone but have impact on the society as a whole through the large costs involved, not to mention the tragedies and the suffering. It should be noted that very little is understood about the true mechanisms associated with head injury, but many theories exist. Implementation or modification of security systems, such as a new helmet, is now a long and complex process. In recent years, biomechanical simulation models of head and human body acquired an increasingly larger place in the design of safety systems. One of the advantages with the finite element (FE) method is the possibility to model the anatomy with great detail, thus it is possible to study the kinematics of the head as well as the stresses and strains in the Central Nervous System (CNS) tissues. This presentation primarily focuses on summarizing current efforts, and to outline future strategies in human head injury prevention in sports. Multiple length scales are involved in the development of traumatic brain injury, where the global mechanics of the head level are responsible for local physiological impairment of brain cells. Prevention through safety helmets with innovative rotational protection systems are demonstrated.

ABSTRACT. Sports-related traumatic brain injury (SR-TBI) is a serious condition which can result in fatal secondary injuries. Finite Element (FE) models have often been used in the context of TBI as an approach to investigate quantities such as stress, strain or energy inside the brain during impact. In sports, however, these efforts are hindered by the fact that accurate kinematic information is difficult to obtain during collisions. Here, we focus on head-to-head collision in sports-like conditions and propose the use of a head and neck model to identify the sporting scenarios from the range modelled with the highest likelihood of inducing SR-TBI. To allow for large scalability and circumvent the computational cost of such large simulations, the FE models are used to train a machine learning layer able to accurately predict the mechanical quantities in the different brain regions of interest. Analysis of these quantities could provide further insight into the mechanisms of SR-TBI itself. We present here the model, the kinematic assumptions and the preliminary results of our approach.

ABSTRACT. Contradictory mechanical responses are a persistent problem concerning experimental studies of ultrasoft materials such as brain tissue when using different testing techniques. These inconsistencies are mainly attributed to the varying testing conditions of the different techniques. Particularly challenging is the use of multiple time and length scales across the experiments. Consequently, a robust identification strategy over a wide strain and frequency range is crucial to achieve reliable mechanical, in particular viscoelastic, parameters of the ultrasoft material. The aim of this contribution is to reconcile the material parameters obtained from experiments that differ in their time and length scales. A phantom material based on oxidized hyaluronic acid (OHA) and gelatin (GEL), showing promising results to mimic the viscoelastic behavior of brain tissue, was used for the measurements. The mechanical behavior of the hydrogel was examined via two testing techniques. At a rheometer quasi-static experiments in the time domain were conducted. The measurements investigated the material behavior in compression, tension and shear. With magnetic resonance elastography the material responses in the frequency domain were obtained. A 0.5T magnet measured the vibrations induced in the material by a piezoelectric actuator. This measurement technique enables to acquire vibration data from a few 100Hz up to several kHz. Aiming at the unification of the mechanical tests in one continuum-based model, the experimental results of both testing techniques are compared by their viscoelastic parameters. The storage and loss modulus are calculated for the experimental data in the time and the frequency domain by viscoelastic standard models resulting from a combination of spring and dashpot elements.

ABSTRACT. Powder compaction is widely used in several industrial fields. This forming process is particularly useful to produce complex net shaped compacts. However, the final structural homogeneity of the compact is, among others, dependent on the material behavior, the complex geometry of the punches used, and the wall friction. Understanding of the development of stress and relative density fields in compaction process is thus a crucial step for improving product quality. The aim of this study was to develop a continuum modelling of pharmaceutical powder compaction process to predict structural inhomogeneity of the compact not only due to wall friction but also to the non-uniform applied pressure linked to the embossed punch surface. The development was applied to special configurations in which the upper and lower punch are identically designed with two or multiple deep trapezoidal grooves. The modelling ambition was to capture the density gradient in between opposite grooves, which was suspected as responsible of the compact damage during the unloading. The powder behaviour was described in the framework of porous mechanics using the phenomenological model of Drucker Prager Cap (DPC) in which material parameters are density dependent and have been determined by means of diametral and uniaxial failure tests and compaction trials in instrumented die. Simulations of the loading and unloading were performed in 2D plane strain using a finite element method and an explicit integration incorporated in the Abaqus software. Predictions of the density gradient between the opposite grooves were validated using X-ray tomography analyses. Results showed a good agreement between predictions and X-ray tomography measurements. They showed also that the multiple grooves promoted more the structural homogeneity of the compact.

ABSTRACT. The context of this study is an investigation for understand agglomerates breakage mechanisms. To do that, experimentations based on agglomerate micro-compressions on tomograph in Anatomix X ray beam line synchrotron Soleil has been carry out. This study is the result of a collaboration between Strasbourg University (Unistra), Anatomix beam line (Soleil synchrotron) and atomic energy office (CEA) teams. These teams pooled their skills for these investigations. The results are in agreement to Kendall’s theory, which argued that the fracture of granule is a consequence of crack nucleation at flaws leading to subsequent crack propagation through the granular structure. The 340µm agglomerate diameter was investigated by one-way cyclic micro-compression test and other agglomerates with a simple load and unload cycle until breakage have been tested. The tomographic post-treatments have enabled the porosities volumes and surfaces created after breakage, the origin of the main crack and its propagation,

ABSTRACT. Three-dimensional contact dynamics simulations are used to study the flow properties of elongated grains in a silo. The grains have a sphero-cylinder shape described by their aspect ratio, which varies from 1 (sphere) to 5 for a thin elongated grain. To ensure accurate statistics, a "perpetual" discharge is simulated for different orifice sizes by 1) reintroducing the exiting grains at the top of the silo and 2) implementing a procedure to break arches when the flow comes to rest, especially for small orifice sizes. As a general observation, when the flow rate Q is plotted as a function of orifice size, it follows a Beverloo-like curve for all shapes. In contrast, for a given orifice size, the flow rate Q is found to vary non-linearly with grain elongation: It first increases to a maximum and then decreases with increasing elongation. Both the packing fraction and velocity profiles are found to be self-similar near the orifice when normalised to the maximum packing fraction and velocity measured at the center of the orifice, respectively. From these profiles, a 3D theoretical expression, inspired by the work of Janda et al [Phys. Rev. Lett. 108, 248001], for the evolution of the flow rate with grain shape is derived, proving that the non-linear variation of Q has its origin in the non-linear variation of the packing fraction with grain shape measured at the centre of the orifice.

ABSTRACT. Cohesive granular materials play a major role in nature and industry. Cohesive interactions between particles have various physico-chemical origins such as capillary bonding, Van der Waals forces, or cementing matrix. Despite extensive experimental and numerical work on these materials, their mechanical behavior under the action of external loading is still poorly understood, and the compaction behavior of cohesive granular materials is highly dependent on the loadings applied. In a previous study we established a link between the material properties, applied force and porosity of a cohesive granular sample submitted to an isotropic compaction [1]. Here we study the influence of the adhesion force under triaxial compression on dense granular samples. We find that shear stress increases linearly with void ratio in the critical state (state of continuous deformation). We show that the cohesive strength is linearly dependent on the adhesion force between the particles. Furthermore, the shear strength and the void ratio are linearly linked in the critical state. We also identify two limiting behaviors in the evolution of the microstructure based on the coordination number and the anisotropy of the contact network: an increase of coordination number at constant anisotropy for the most cohesive cases, and an increase of anisotropy at constant coordination number for the least cohesive cases. We show that these two microstructural parameters are linked together in the fabric space as a result of steric exclusions. [1] : M.Sonzogni, J.M.Vanson, Y.Reynier, S.Martinet, K.Ioannidou and F.Radjai, Soft Matter, submitted on 12/2023

ABSTRACT. Research of free vibrations of porous functionally graded material (FGM) plates with complex shape is carried out. It is supposed that thickness of the plate changes in direction of one of the axes. Two types of porosity distributions through the thickness even and uneven are considered. To obtain the mathematical model of the given problem the first order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction is modelled by the power law. Variational Ritz’s method joined with the R-functions theory is used for solution of the formulated problem. The developed approach is tested on a lot of problems. Comparative analysis of the obtained results for rectangular plates confirms their verification. Demonstration of the efficiency of the proposed approach is fulfilled for FGM plate with complex shape and various boundary conditions. Effect of the different parameters on vibration characteristics such as porosity, volume exponent, types of FGM, boundary conditions is studied.

ABSTRACT. The commercialisation of solid-state lithium-ion batteries is currently hampered by the phenomenon of lithium dendrite growth across the ceramic electrolyte upon battery charging. In order to mimic the mechanical environment experienced by lithium dendrites, compression experiments have been performed on thin lithium layers sandwiched between ceramic substrates. These experiments reveal that the average pressure on the lithium layer increases with decreasing layer thickness, due to a combination of plastic constraint and size effect. Shear experiments have also been conducted and they reveal a moderate size effect. Strain gradient plasticity is used to explain and predict size effects in both compression and shear. It is assumed that lithium behaves as a rigid, plastically incompressible, power law creeping solid, and that the effective plastic strain rate depends on the plastic strain rate gradient through a single plastic length scale. Approximate analytical solutions are obtained for an assumed velocity field by energy minimisation. Full numerical solutions are also obtained to verify analytical solutions. For compression of specimens of high aspect ratio, the analytical solution shows that the enhancement in average pressure due to plastic constraint and size effect can be decoupled in a multiplicative manner. The best match between theory and experiments is obtained by assuming fully constrained higher-order boundary conditions and for a plastic length scale on the order of a few microns.

ABSTRACT. Recognizing the significance of Geometrically Necessary Dislocations in modeling size effects, kinematic hardening has been incorporated into higher-order Strain Gradient Crystal Plasticity (SGCP) through two separate approaches. The proposed models are based on the decomposition in series of the gradient of the plastic slip which helps modeling higher-order dissipation while avoiding the production of elastic gaps [1] as found with the original Gurtin approach. The first model involves multiple decomposition of the gradient of the plastic slip into reversible and dissipative parts resulting in a kinematic stress that equals the sum of various stresses. This theory is linked to the kinematic hardening modeling approach of Chaboche. The second model employs only one serial decomposition but includes a higher-order Prager kinematic hardening, which depends on the dissipative part. A shared characteristic of these models is the use of less-than-quadratic defect energy as there is no experimental evidence to support the classical quadratic form. In this study, the SGCP formulations introduced, aim to replicate size effects observed with Discrete Dislocation Dynamics under 2D shear loading. More specifically the focus is put on strengthening and the uncommon Asaro’s type III kinematic hardening. In the continuum formalism, the later observation is purely the outcome of a non-quadratic form of the defect energy. The proposed models are then used to investigate size effects experimentally observed by Zhang et al. [2] in combined bending-torsion of a FCC single crystal.

[1] Y. A. Amouzou-Adoun, M. Jebahi, M. Fivel, S. Forest, J. S. Lecomte, C. Schuman, and F. Abed-Meraim. On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation. Acta Materialia, 252:118920, 2023. [2] B. Zhang, K. L. Nielsen, J. W. Hutchinson, and W. J. Meng. Toward the development of plasticity theories for application to small-scale metal structures. Proceedings of the National Academy of Sciences, 120(44):2017,2023.

ABSTRACT. The regularizing properties of gradient models for the simulation of plasticity localization problems are well known. In the case of crystal plasticity, they classically rely on a constitutive theory with a dependence on a tensorial measure of geometrically necessary dislocations (GNDs) density, associated to a length scale parameter. This length scale allows to control grain size effects on hardening induced by GNDs, but also to regularize the formation of kinks bands. However, this theory cannot yield a regularization of slip bands formation, due to the lack of dependence on the plastic distortion gradients components that are not associated to GNDs. In this work, we present a gradient crystal plasticity framework that introduces a dependence on a second tensorial measure of plastic slip gradients, associated to a second length scale parameter that yields a regularization of slip bands. The framework has been implemented within the FFT-based solver AMTIEX_FFTP. Analytical calculations and numerical simulations of single crystals and polycrystals will be presented. Our results show that these two length scales allow to control the characteristic size of slip and kink bands independently, and influence the competition between slip and kink banding. As a result, this framework allows capture important features of observed slip band networks in polycrystalline materials within crystal plasticity simulations. Finally, perspectives towards its application for the modeling of slip localization induced fatigue cracks will be discussed.

ABSTRACT. This study investigates the numerical implementation of strain gradient crystal plasticity theory using the Fast Fourier Transform (FFT)-homogenization method for irradiated polycrystalline aggregates subjected to tensile loading. The formulation of strain gradient crystal plasticity is established to enhance the accuracy of the results compared to classical crystal plasticity, especially in cases where strain localization bands emerge. In particular, various nonlocal parameters are introduced and types of generalized boundary conditions applied to grain boundaries when solving the generalized balance equation, which is derived by the principle of virtual power together with linear momentum balance equation (Cauchy’s equation of motion). These boundary conditions, commonly known as micro-free, micro-continuity, and micro-hard, improve the control of dislocation transmission between the neighboring grains. The study also explores the influence of irradiation on the realistic type of microstructure, such as Voronoi polycrystalline aggregate, by analyzing the formation of localization bands, commonly referred to as “clear channels”. The simulations reveal two distinct types of localization bands: slip bands (aligned with the active slip system) and kink bands (rotated with respect to the active slip system). Computationally, to obtain the results, a fixed-point algorithm (basic scheme) is employed to address the proposed micromechanical model of classical crystal plasticity within the FFT-homogenization framework. However, a pseudo-explicit algorithm is utilized for strain gradient crystal plasticity. To enhance the performance, the algorithm is enriched by the rotated scheme for the Green operator and a specific variant of the Anderson acceleration known as the alternate 2-δ method. Both enrichments accelerate the convergence and refine the results. Furthermore, going beyond the linear momentum balance equation, the resolution of the generalized balance equation in the context of strain gradient crystal plasticity theory incorporates a 21-voxel finite difference scheme due to its superior performance in regions characterized by strong discontinuities such as grain boundaries.

ABSTRACT. In recent years, various data-driven methods have been developed in the field of computational mechanics. Data-driven mechanics, introduced by Kirchdoerfer and Ortiz [1], replaces conventional material modeling with data-sets containing snapshots of stress and strain assumed to be sufficiently accurate representations of the underlying material behavior. Build on these snapshots, termed material states, and on states fulfilling equilibrium and kinematic compatibility, denoted mechanical states, is a distance function, the minimization of which with respect to both of these states yields the boundary value problems’ solution.

Originally introduced for elasticity, the extension to inelasticity poses a significant challenge and different approaches have been proposed in literature. Our extension allows to preserve the spirit of the original method so that no real-time adjustments of the data-set are required. We achieve this by storing essential information of the history in a history surrogate and update this quantity at the end of each time step using a propagator. Finding suitable choices of these quantities can be challenging. By utilizing a Neural Network as propagator, we can let the Network tackle this task autonomously without resorting to a material model.

In this contribution, we present simulations for both a neural network and an intuitive propagator. We highlight the capabilities of our extension and provide a discussion of the obtained results. The neural network enhancement allows for an automated framework for which we show the necessary training routines and the results of which we compare to those of an intuitive choice of history surrogate an propagator.

[1] T. Kirchdoerfer, M. Ortiz, Data-driven computational mechanics, Comput. Methods Appl. Mech. Engrg. 304 (2016) 81-101 [2] T. Bartel, M. Harnisch, B. Schweizer, A. Menzel, A data-driven approach for plasticity using history surrogates: Theory and application in the context of truss structures, Comput. Methods Appl. Mech. Engrg. 414 (2023), 116-138

ABSTRACT. Fiber-reinforced concrete (FRC) is a composite material where small fibers made from steel or polypropylene or similar material are embedded into concrete matrix. In a material model each constituent should be adequately described, especially the interface between the matrix and fibers that is determined with the 'bond-slip' law. 'Bond-slip' law describes relation between the force in a fiber and its displacement. In order to accommodate variations in experimental results we have adopted stochastic model that is based on the 'fiber bundle representation'. The initial stochastic model formulation has been generalized into a two-parameter exponential material model that has been used as a basis for a simple three-point beam-bending model. In addition, laboratory experiments of three-point beam bending have been performed with an intention of using experimental data for determination of material parameters. It is not possible to use 'forward' beam model for extraction of material parameters so an inverse model has been devised. The inverse model is an iterative procedure based on derivative of experimental data and has successfully recovered the initial material parameters.

ABSTRACT. The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic or quasi-linear viscoelastic models [1]. These popular models are simplifications that typically cannot accurately capture the nonlinear viscoelastic behavior of materials. For example, the success of attempts to capture strain (rate)-dependent behavior has been limited so far. In response to this issue, we introduce viscoelastic Constitutive Artificial Neural Networks (vCANNs), a novel physics-informed machine learning framework [2]. vCANNs rely on the concept of generalized Maxwell models with nonlinear strain (rate)-dependent properties represented by neural networks. With their flexibility, vCANNs can automatically identify accurate and sparse constitutive models for a wide range of materials. To assess the capabilities of vCANNs, extensive training was conducted using experimental stress-strain data from synthetic and biological materials subjected to diverse loading conditions, e.g., relaxation tests, cyclic tension-compression tests, and blast loads. The results show that vCANNs can learn to accurately and efficiently represent the behavior of these materials without human guidance. We showcase the seamless integration of vCANNs into existing finite element codes through illustrative examples. This integration underscores the practical applicability of vCANNs in the field of applied mechanics.

References

[1] K. Linka et al. [2021], 'Unraveling the local relation between tissue composition and human brain mechanics through machine learning', Frontiers in Bioengineering and Biotechnology 9:704738 , https://doi.org/10.3389/fbioe.2021.704738. [2] K.P. Abdolazizi, K. Linka, C.J. Cyron [2023], 'Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticity', Journal of Computational Physics 499:112704, https://doi.org/10.1016/j.jcp.2023.112704.

ABSTRACT. In the sense of the process-structure-property chain, to add value to the development of new advanced materials, materials design approaches must be tailored to support downstream optimal processing approaches. In this contribution, we combine recently developed data-driven machine learning-based approaches to address two critical identification problems: (1) a materials design problem, which identifies near-optimal material microstructures for desired properties, and (2) a process design problem, that aims to guide manufacturing processes to produce identified microstructures. Both identification problems are ill-posed inverse problems and are therefore, typically non-unique (i.e., more than one solution exists). This offers an advantage which is leveraged in the machine learning-based approaches to guide the underlying manufacturing process efficiently to produce the best reachable microstructures. The approaches presented are demonstrated at the example of a simulated metal forming process, aiming to optimize crystallographic texture.

ABSTRACT. The notion of Data Driven Computational Mechanics (DDCM) has been introduced in Kirchdoerfer and Ortiz, CMAME 2016, where the behavior of the material is described by the stress-strain database obtained from the experiments or through the simulations performed at a lower scale. This database is directly used in Finite Element simulations, for instance, rather than using a constitutive model to describe the material behavior. The DDCM methodology has been applied for linear, non-linear elasticity, and inelasticity in multiple references. However, its application to scenarios involving softening remains relatively open. In applications that involve softening, a characteristic length is necessary to render the results of the Finite Element simulations independent of the mesh size. In the case of granular materials, the length scale has been introduced in DDCM by treating the material as a Cosserat medium. However, this technique is effective only when the body is subjected to a shear loading. To introduce a length scale in a general scenario, a strain-based Lipschitz regularization has been introduced in an earlier study. The contribution of the current work is to include the Lipschitz regularization technique in the DDCM methodology for applications that involve damage. This work first presents the regularization technique followed by its application to some test cases. Some challenges encountered and future perspectives will be presented.

ABSTRACT. Extruded foods from pulses can be envisaged as solid foams with cell walls, considered as a dense starch-protein composites. Pea flour (PF) and blends of pea starch and pea protein isolate (PPI) with different protein contents (0.5-88% dry basis) were extruded under various thermomechanical conditions (Specific Mechanical Energy=102-103kJ/kg) to obtain models of dense starch-protein composites with different morphology. Their morphology was revealed by CLSM microscopy, and their mechanical properties were investigated using a three-point bending test, complemented by Finite Element Method (FEM) modelling. Composite morphology revealed protein aggregates dispersed in the starch matrix. It was described by a starch-protein interface index Ii computed from the measured total area and perimeter of protein aggregates. The mechanical test showed that the extruded PF and PPI ruptured in the elastic domain, while the extruded starch-PPI (SP) blends ruptured in the plasticity domain. The mechanical properties of pea composites were weakened by increasing the particle volume fractions, including proteins and fibres, probably due to the poor adhesion between starch and the other constituents. The mechanical behaviour of pea composites did not accurately follow simple mixing laws because of their morphological heterogeneity. Modelling results show that the elastoplastic constitutive model using the Voce plasticity model satisfactorily described the hardening behaviour of SP blend composites. Reasonable agreement (2-10%) was found between the experimental and modelling approaches for most materials. The computed Young's modulus (1.3-2.5 GPa) and saturation flow stress (20-45 MPa) increased with increasing Ii (0.7-3.1), reflecting the increase of interfacial stiffening with the increase of contact area between starch and proteins. FEM modelling was shown to be a relevant approach to consider the microstructure heterogeneity of starch-protein composites, and to contribute to the design of extruded pea products with desired properties.

ABSTRACT. Nowadays, about 15% of people living in post-war countries needing prosthetic and orthotic equipment they have access due to their long, high costs and complex manufacturing processes. In recent years, additive manufacturing (AM) is increasingly popular in the rehabilitation centers as an alternative since prototypes can be manufactured without resorting to the manufacture of expensive molds. However, 3d printing of orthopedic devices is still primarily based on a trial-and-error experiments, leading to waste and a high material and time-consuming. Therefore, we investigated the possibility of utilizing virtual AM environment to identify the critical points of lower limb prostheses, which are otherwise difficult to obtain with physical tests, and thus avoid errors while making adjustments upstream during their design. The present work aims to explore and evaluate the fused deposition modeling (FDM) process as an affordable technology to build high performance transtibial prosthesis devices based on Acrylonitrile butadiene styrene (ABS) using a combined numerical and experimental approaches. To do that, a numerical workflow was implemented starting from a 3D scan of the patient stump. Then, through reverse engineering, we created a 3D model necessary to manufacture the socket and the junction base of the equipment. The topological optimization was then performed by taking into account the mechanical properties of the ABS material and the stresses generated during gait cycle phases. The FDM process was then simulated through the Digimat® AM software to measure the impacts of material and printing parameters on the warpage of the as-printed parts. Thereafter, structural analysis was carried out, taking into account the FDM process history which allows the prediction of mechanical strength and deformations of prostheses under different gait loading efforts. Finally, a metrological control was deployed on the optimized geometrical 3D printed parts by comparing the numerical results with the experimental 3D scan data.

ABSTRACT. 3D printed polymer materials present a growing interest in a number of fields including aerospace, energy, construction industries, as well as bioengineering applications [1]–[3]. While conventional molded or extruded polymer materials are well known and characterized via standardized procedures, this is not the case for 3D printed polymers. More precisely, it is of prime importance to better understand the influence of the 3D photopolymerization process and resin chemistry on the final mechanical properties of the object [4]. In our work, we formulated in-house acrylate resins with controlled resin chemistry. The resin physico-chemical properties and their printability were fully characterized. In particular, we investigated the influence of the nature of the acrylate monomer on the resin properties. Besides, after successful printing, the resin mechanical properties were investigated via Dynamic Mechanical Analysis (DMA) in flexion to determine the elastic modulus of the final materials. The results were compared to a molded analog acrylic polymethyl methacrylate (PMMA) and to commercial resins. We observed that by tuning the resin formulation and optimizing the printing process, it is possible to achieve PMMA-like stiffnesses with 3D printed pure acrylate resins. A statistical analysis was also performed, revealing a greater dispersion of the results in terms of reproducibility for 3D printed materials (both commercial and formulated resins) with respect to that in molded PMMA. However, our homemade resins have a lower dispersion than commercial resins, which underlines the importance of controlling both resin chemistry and printing parameters.

References: 1. Zhang, F. Addit. Manuf. 48, (2021). 2. Zhang, J., Int. J. Bioprinting 6, 12–27 (2020). 3. Al Rashid, A., Processes and applications. Addit. Manuf. 47, 102279 (2021). 4. Schittecatte, L., MRS Commun. 13, 357–377 (2023).

ABSTRACT. Extrusion-based additive manufacturing (EB-AM) technologies are one of the most widely used 3D printing technologies. In recent years, this technique has moved a step further towards the so-called 4D printing. This new term allows not only the control of structural characteristics of the components but including other functionalities with properties that vary in space and/or time. To obtain this extra performance, the polymeric matrices are reinforced with particles. This idea is enabled by different EB-AM technologies that use a starting material in a semi-liquid state, e.g.: FFF that melts polymeric filaments during the extrusion; or DIW that uses a pre-cured polymeric “ink”. All these techniques involve extrusion through a nozzle and, therefore, the material viscosity and its temporal evolution during printing is crucial. This needs to be sufficiently low to facilitate extrusion and the coalescence with other filaments but, at the same time, high enough to ensure shape fidelity. With the aim to understand the mechanics of the coalescence between printed filaments and the role that viscosity and surface tension play in the process, we propose a hybrid experimental-computational methodology. We first develop an experimental campaign to record the filament coalescence depending on the material used, and with a special focus on those whose rheological properties evolve over printing time [Lopez-Donaire et al., Adv. Mat. Tech. 2023]. Then, we propose a phase-field model with time-dependent properties that describes the dynamics of two non-miscible phases (material printed and surrounding medium). This methodology allows for identifying the optimal parameters of the printing process. Acknowledgment: The authors acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947723, project: 4D-BIOMAP). S. Garzon-Hernandez acknowledges support from the Talent Attraction grant (CM 2022 - 2022-T1/IND-23971) from the Comunidad de Madrid.

ABSTRACT. Polyether-ether-ketone (PEEK) stands out as a semi-crystalline engineering thermoplastic uses in many industries such as automotive, aerospace, and medical sectors. This material now solves the challenges of customized medical scaffolds through promising results of nontoxicity, high mechanical strength, lightweight nature, biocompatibility, and resilience at elevated temperatures. The main drawback of PEEK is printability. The common procedure to print PEEK components is Fused Deposition Modeling (FDM) has many process parameters to adjust. Changing the 3D working parameters in PEEK FDM significantly influences mechanical strength and product quality, presenting a common challenge in ensuring high-quality and robust outputs. This challenge needs to be addressed specifically when PEEK supports complicated surgery and in the construction of customized artificial implants. This research introduces an innovative modeling approach employing artificial neural network (ANN) and an elitist genetic algorithm (GA) to optimize process parameters to enhance the mechanical strength of PEEK printed components. The wide range of nozzle and bed temperatures, print speeds, and layer thicknesses are investigated thoroughly. SEM microstructure analyses of specimens printed with varied parameter values further enrich the comparative evaluation. The result reveals the best possible options to print PEEK materials. By optimizing adjustable parameters crucial to mechanical strength using genetic algorithms, the study compares results with existing literature and previous Taguchi orthogonal array designs. The proposed methodology extends beyond mechanical strength investigation, offering insights applicable to diverse mechanical properties.

ABSTRACT. Structural health monitoring of aerostructures translates into a significant reduction in maintenance costs as well as lighter, more efficient component designs by providing real-time insight into the remaining lifespan throughout the whole life cycle. To perform this monitoring, the structure is required to be instrumented with a robust and sufficiently sensitive sensor system.

This work focuses on one of the most relevant applications of these systems, low energy impact damage localization. To this purpose, the monitoring relies on a mature technology, strain gauges. Thermoplastic PAEK/CF panels are instrumented with an array of gauges and tested under three-point bending conditions in pristine and impacted conditions.

In the deformed state, it is possible to compare the effect of damage in the strain field by means of its point values measured by strain gauges, using these compared values to infer damage extension. This is achieved through an artificial neural network trained on synthetic data generated by an accurately calibrated finite element simulation, this approach is known to be efficient in surrogate modelling of composites [1].

The resulting trained model performs as a digital twin of the composite panel, being able to predict with accuracy the location of impact as well as distinguish the impact energy that caused the damage. Several densities of strain gauges arrays are studied to assess the sensitivity of the monitoring system, while in-service robustness is achieved by ensuring the model performs effective predictions with malfunctioning gauges.

[1] J. Fernández-León, K. Keramati, C. Miguel, C. González, L. Baumela - A deep encoder-decoder for surrogate modelling of liquid moulding of composites. Engineering Applications Of Artificial Intelligence 120, 105945-105945, 2023.

ABSTRACT. Voids are one of the most common, and arguably most critical, manufacturing defects in composites. They are difficult to avoid and detrimental to composite performance. Research has indicated that void morphology significantly influences failure, but difficulties in understanding these influences has resulted in industry implementing conservative part rejection criteria based on average void content. To maximise material utilisation, and reduce material waste, it is crucial to adopt an approach that takes these factors into account when assessing the impact of voids on composite strength. Currently, finite element (FE) methods are widely employed to predict the performance of laminates with voids. FE modelling of samples with voids can be at the micro-scale or meso-scale, and is generally computationally expensive due to the need for refined meshes around voids. In this study, deep learning, specifically convolutional neural networks (CNN), was applied to experimental data in order to predict the short beam shear strength of the composite materials with voids. A total of 230 samples were manufactured using two commonly used material systems (Hexcel’s IM7/8552 and IMA/M21). All samples were CT-scanned prior to testing. Two CNN approaches were investigated: the first approach involved deep CNN networks with varying architectures and complexities, the second approach involved CT-Scan parametrisation using autoencoders that are subsequently coupled with a Gaussian Process surrogate to predict material strength. Several parameters were analysed to optimise the performance of the CNN, including learning rate, mini-batch size and CT-Scan resolution. A 5-Fold cross-validation approach was used to evaluate the network performance, and the results demonstrated that deep learning holds significant potential in strength prediction of composites with voids.

ABSTRACT. This research explores the fracture properties of thermoset IM7/8552 composite materials, focusing on translaminar behaviour. Cross-ply laminates with a [0°/90°]6s configuration were crafted via autoclave consolidation, resulting in a 5.9 mm thickness and a 57.4% nominal fiber volume fraction. Four Compact Tension specimens, featuring well-defined pre-crack tips, were extracted for fracture tests under displacement control. A compliance calibration (CC) method established crack resistance curves using instantaneous critical load values to track fracture propagation and calculate energy release rates. The compact tension specimen's 2D geometry underwent finite element discretisation, modelling fracture behaviour with a 0.1 thickness layer of cohesive elements. Constitutive behaviour of cohesive elements followed linear (LCL) and bilinear (BCL) softening laws. The material behaviour included parameters like elastic modulus (E) and specific softening curve parameters. For the linear case (LCL), the parameter set was ΘLCL = [E, XT, GIC]. A superposition technique was used in the bilinear softening curve (BCL), obtaining ΘBCL = [E, XT, GIC, n, m]. 200 cases, each with distinct parameters drawn from uniform random distributions, were generated for virtual fracture tests in Abaqus Standard, collecting displacement (δ), load (P), crack growth (∆a), and computed GI. An artificial neural network (ANN) connected the input fracture parameter dataset with FEM-obtained load-displacement, crack-displacement, and dissipated energy-displacement. Normalising both datasets to a non-dimensional scale (0, 1) enhanced ANN accuracy. Discrepancies between actual and predicted load-displacement and crack-displacement curves for unseen test data consistently stayed below 1.5%, affirming a strong agreement between ground truth and surrogate model predictions. This underscores the surrogate's efficacy in providing a rapid and dependable response.

ABSTRACT. Composite materials are favored due to their exceptional strength-to-weight ratios. However, their weak interfacial characteristics make them vulnerable to out-of-plane loadings, including low-velocity impact (LVI). The increasing interest in numerical simulations for assessing composite resistance to LVI necessitates validation through direct damage observations. In a recent experimental study by Bozkurt and Coker (2021), [05/903]s CFRP beam specimens subjected to transverse impact loadings where strain fields are measured using the digital image correlation method, and damage evolution is captured in situ using an ultra-high-speed camera. In this study, we constructed the high-fidelity finite element (FE) model of the LVI experiments conducted by Bozkurt and Coker. The simulations utilize a user-implemented three-dimensional continuum damage model with the LaRC05 criterion for matrix cracking, and a built-in cohesive zone model for delamination in ABAQUS/Explicit. The influence of boundary supports on the global response is found to be significant, therefore, a heuristic boundary conditions approach that replicates the experiment boundaries through the assembly of spring elements is proposed. The simulation results then demonstrated excellent agreement with the experiments in terms of global impact response and damage pattern and sequence. Simulations reveal delamination propagation with crack tip speeds around ~5000 m/s, while experimental delamination crack tip speeds were measured at ~1000 m/s. However, when a crack tip definition based on the crack opening is introduced in the simulation, crack tip speeds in the range of 490-1500 m/s are measured consistent with experiments, implying that the sliding mode might be physically hidden in the experiments. Increasing the effective interface toughness to incorporate the macroscopic effects of experimentally-observed microscopic cracks at the interfaces demonstrated the potential use of delamination crack tip speeds as a benchmark for refining numerical simulations.

ABSTRACT. In this study, we subjected polymer slabs with three-dimensional porous Bouligand structures to stab tests, to investigate the influence of the pitch angle and spacing on the stab resistance and fracture of the Bouligand structure. Stab tests were conducted following the HOSDB/P1/B (UK) standard, and the porous Bouligand structured polymer samples were additively manufactured using a Form3 SLA 3D printer. Here, we consider the stab resistance characteristics of porous structures by normalising them against solid (non-porous) polymer material and compared them against the material's relative density. CT microtomography scans were utilised to identify damage profiles, which were then analysed internally through 3D image analysis techniques. Finally, optical methods were employed to analyse the knife penetration depth and damage footprint, aiming to identify critical criteria for stab resistance.

ABSTRACT. Additive manufacturing (AM) enables the creation of intricate, customizable geometries such as cellular lattices with customizable mechanical behavior. This method results in materials with unprecedent properties, reduced waste, minimized economic impact and shorter manufacturing durations. This is particularly the case for new high-energy absorption metamaterials for dynamic applications.

However, there are still gaps in knowledge around the effect of cell design, processing defects and dynamic behavior of cellular lattice materials. Understanding the effects of lattice architecture and processing on the mechanical behavior under high strain rates is crucial for enhancing the energy absorption of these cellular materials under extreme conditions.

This study investigates the dynamic behavior of Ti6Al4V cellular lattice structures manufactured through Laser Powder Bed Fusion (LPBF) from a multiscale approach: from the high strain rate behavior of their individual strut elements to the overall macroscopic dynamic behavior of the architected lattice. The technique used is the Split Hopkinson Pressure Bar technique. Design and processing variables like strut diameter and printing orientation are accounted for.

The research highlights a strong correlation between strut diameter, printing orientation, dynamic strength, toughness, and failure mode both within the lattice structures and the elemental struts. For single elemental struts, observations indicate that smaller strut diameters lead to increased strength but reduced ductility and energy absorption. Regarding the printing orientation, the study shows a general drop in mechanical properties as the printing angle tilts. For the case of the macroscopic behavior of lattices, dynamic tests reveal an enhanced energy absorption in lattices with larger strut diameters but a more ductile fracture mode with increased homogeneous deformation across all the struts for smaller diameters.

Grant PID2020-116440RA-I00 funded by MICIU/AEI/10.13039/501100011033. Grant EQC2019-006491-P funded by MICIU/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”. Grant PRE2021-097388 funded by MICIU/AEI/10.13039/501100011033 and by “ESF+”.

ABSTRACT. According to the progress in 3D printing, manufacturing of parts with complex patterns became very interesting in the development of specific panels for various industrial applications, from construction to aeronautics. In this work, the effect of elevated temperatures on the mechanical properties of lattice core sandwich panels was studied for better understanding of their thermomechanical behavior. First, mechanical properties of certain cellular topologies were compared to those of the traditional sandwich plates with honeycomb core. Then, an ABAQUS numerical thermal model for a pyramidal lattice core panel was developed. This model was then validated for a composite lattice core panel made of a silicon carbide matrix with carbon fiber reinforcement (C/SiC composites), through comparison between results obtained by numerical simulation versus experimental results. Lastly, the numerical model was then used to optimize the mechanical properties of a pyramidal lattice sandwich panel made of glass fiber epoxy composite when subject to a temperature of 200 °C on a single surface.

ABSTRACT. This study presents a comprehensive investigation of bidirectionally sinusoidal corrugated steel shells using advanced finite element analysis (FEA) software, primarily ABAQUS, supplemented by RFEM for initial result comparison. The research aims to establish a robust numerical solution, unravelling the intricate structural behaviour of these shells under static and dynamic loading conditions.

This study initiates with the execution of meticulous calculations for a carefully selected structural element, providing a comprehensive foundation for subsequent analyses. The paper places emphasis on a comparative analysis between ABAQUS and RFEM, offering valuable insights into their respective roles in simulating the response of bidirectionally sinusoidal corrugated steel shells.

Moreover, the investigation systematically explores an array of model parameters, including variations in geometrical and mechanical properties. Through detailed analyses and rigorous comparisons, the research elucidates the nuanced influence of these parameters on critical aspects such as deformation, stress distribution, and dynamic behaviour exhibited by the corrugated steel shells.

A distinctive feature of this research involves the development and utilization of a coded script. This script enables the systematic generation of a diverse array of numerical models, allowing for a thorough exploration of the structural system's response.

In conclusion, this study significantly contributes to advancing the understanding of bidirectionally sinusoidal corrugated steel shells' structural behaviour. By leveraging the capabilities of ABAQUS and thoughtfully integrating RFEM for preliminary comparisons, the research provides valuable insights into the simulation of complex structural systems. These findings are poised to elevate current structural analysis and design practices, particularly by optimizing geometrical and mechanical parameters for the enhanced performance of these innovative structural elements across a spectrum of engineering applications.

ABSTRACT. Periodic lattice structures are increasingly used to achieve functions such as shock absorption, wave propagation, wave guiding, and/or programmable materials. The design of such systems calls for effective continuous homogenized models capable of precisely capturing the mechanical behavior of these complex periodic or quasi-periodic microstructures [VP12]. We propose a versatile and systematic method for deriving higher-order asymptotic continuum models for periodic beam networks. It yields a homogenized energy that is asymptotically exact two orders beyond that obtained by classical homogenization [AL23]. Our homogenization method is applicable to various types of networks, in 2D or 3D and we validate it by comparing the predictions of the microscopic displacement to that obtained by full discrete simulations. When used incrementally, the method extends to lattices subject to finite deformation. We take the 'triangular–hexagonal'-Kagome lattice as an example. It features zero-energy modes [NCH20] and under finite deformation, the solutions are close to a mechanism with small deviations that are sensitive to the gradient effect, which motivates us to model this microstructure with our gradient theory. In the presentation, we present the effective nonlinear energy for the Kagome lattice and we investigate how it captures gradient effect for a given boundary value problem. Bibliography [VP12] Andrea Vigliotti and Damiano Pasini. Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials. Mechanics of Materials, 46:57–68, 2012. [AL23] B. Audoly and C. Lestringant. An energy approach to asymptotic, higher-order, linear homogenization. Journal of Theoretical, Computational and Applied Mechanics, 2023. [NCH20] Hussein Nassar, Hui Chen, and Guoliang Huang. Microtwist elasticity: a continuum approach to zero modes and topological polarization in kagome lattices. Journal of the Mechanics and Physics of Solids, 144:104107, 2020.

ABSTRACT. Near-field detonation of high explosives liberates a large amount of energy in a short time and exerts high localized forces on the interacting structure. Sandwich panels with energy-absorbing cellular materials in the core, that dissipate the blast energy by undergoing progressive plastic deformation, have been widely used as sacrificial cladding. Conventional core materials with positive Poisson’s ratio exhibit localized resistance against localized loading allowing only a small volume of core to participate in energy dissipation. However, auxetic materials possess a Negative Poisson’s Ratio (NPR), allowing them to undergo lateral contraction during a longitudinal compression, engaging more volume of the core that can participate in the dissipation of blast energy. This research investigates the application of a Re-entrant Honeycomb Sandwich Panel (RHSP) as protective cladding beneath an armoured vehicle to counter an underbelly blast. It also examines the influence of shape variables of a re-entrant unit cell: the re-entrant angle (θ), the horizontal length (L), and the slant length (D) on the blast response. Besides shape variables, the effect of variation in the number of core layers was also analyzed. TCL scripting was used to generate automated Finite Element (FE) models based on different values of shape variables. It was observed that the collapse kinematics of the auxetic core varies for different values of shape variables. This contributes significantly to the amount of material being recruited in the impact zone and consequently the energy absorbed by the auxetic sandwich panel and the force transmitted to the armoured vehicle.

ABSTRACT. It is widely agreed that additive manufacturing is currently at a stage where a comprehensive knowledge of its processing parameters, microstructure and mechanical behaviour relationship is needed to advance into a more general implementation. However, this task is particularly complex for this technology due mainly to the extreme process conditions. A novel coupling between a continuous wave laser and an environmental scanning electron microscope can turn out to be a very valuable tool to help accomplish the aforementioned task. In fact, it allows process characterisation and parameter control, enabling the development of the technology. Furthermore, post processing and surface treatment can also be developed with this device. A practical example of the potential of the laser SEM coupling is the mechanical behaviour enhancement of laser metal deposition 316L steel. The device was used to post process and characterise this material. Microstructural refinement and surface roughness reduction were achieved. In consequence, a very significant strengthening, without ductility loss, and fatigue resistance improvement were obtained. These results convey in an unprecedented manner the potential of lasering for microstructure enhancement.

ABSTRACT. The energy sector uses a large amount of moving metallic parts, for example stainless steel pumps or collectors. Such kind of parts can be damaged during the use life and small cracks can appear after some years. Classically, the cracks are manually repaired with welding techniques leading to large internal stresses. In this study, we have developed repairs by using direct metal deposition. The impact on the substrate has been studied and a robust process window has been defined. The quality of the repair is excellent in terms of level of porosity, chemistry and mechanical properties. Moreover, the automation of this process will be presented.

ABSTRACT. Fe-based soft magnetic bulk metallic glasses (BMGs) have shown unprecedented magnetization saturation and coercivity values and are thus envisioned as potential candidates to increase the efficiency of electromagnetic components. Laser powder bed fusion (LBPF) allows to manufacture relatively large BMG parts while retaining an amorphous microstructure due to high local cooling rates. However, in practice, the thermal cycles generated in the layer-wise LBPF process tend to cause undesired crystallization, which hinders the magnetic properties of printed parts. In general, the processing parameters that yield the densest prints also cause severe crystallization upon solidification. On the other hand, the parameters that allow the material to retain the amorphous microstructure tend to leave structural defects, mainly due to lack of fusion. To date, complex LPBF scanning strategies, which are difficult to replicate, have been the most successful avenue to avoid crystallization of BMG’s during fabrication. However, the fundamental relationship between processing parameters, defects, (micro)structure and properties, still remains unclear for many BMG compositions.

This work aims to provide a thorough study of the individual effect of the main LPBF processing parameters (laser power, scaning speed, and hatch distance) on the resulting (micro)structure and mechanical and magnetic properties of a commercial Fe-based BMG alloy. The feedstock amorphous powder is processed using a pulsed-wave laser system and a simple scanning strategy. Complementary experimental techniques such as image analysis, X-ray diffraction (XRD), differential scanning calorimetry (DSC), electron backscatter diffraction (EBSD) and mechanical and magnetic testing were used to characterize the evolution of (micro)structure and magnetic properties. This study defines guidelines for the successful additive manufacturing of Fe-based BMGs by pulsed laser powder bed fusion.

ABSTRACT. The ongoing energy crisis demands extensive research into new alternatives for enhancing the energy efficiency of electric motors. As a probable solution to this, soft magnetic materials (SMM) portray excellent properties with high saturation flux density (BS) and low coercivity (HC)[1]. SMMs possess the ability to cater to this need, as they can substantially increase the efficiency of electric motors by reducing the core losses. Although promising, soft magnetic Fe-based amorphous metals need further research to overcome production challenges, as the need for high cooling rates to generate a significant fraction of the amorphous phase severely limits their production to thin ribbons resulting from rapid solidification processes such as melt spinning. Earlier work on additive manufacturing (AM) parameter optimization of a Fe-Si-B-based bulk metallic glass (BMG) has, however, shown promise for the fabrication of relatively large net-shape rotors [2]. This work investigates the effect of thickness on the (micro)structure and the magnetic behavior of Kuamet6B2 samples. The optimum combinations of parameters that fared well in terms of overall part density and amorphous degree of bulk samples have been applied in the current work to manufacture walls with thicknesses ranging from 500 µm to 1500 µm by laser powder bed fusion (LPBF). In particular, the wall thickness is correlated with the density, the defect structure, the meltpool morphology, the degree of amorphicity, and magnetic properties such as saturation magnetization (Js) and coercivity (Hc). To achieve this, complementary structural characterization techniques, including scanning electron microscopy (SEM), X-ray diffraction (XRD), and differential scanning calorimetry (DSC) have been utilized in conjunction with image analysis tools. The magnetic behavior was characterized using a vibrating sample magnetometer (VSM). The outcome of this work will provide guidelines for the design of soft magnetic bulk metallic glass components with more complex geometries and improved energy efficiency.

ABSTRACT. Over recent years, manufacturing of tool steels by Laser Powder Bed Fusion (LPBF) has been the object of increasing attention for the possibility of producing parts, with complex shape difficult to obtain through conventional methods. Moreover, the ultra-fast heating and cooling rates pertaining to the LPBF process are responsible for the formation of strongly out-of-equilibrium microstructures, involving supersaturated solid solution and new metastable phases, thus offering new possibilities in terms of usage properties. Therefore, research is now focusing on the development of tool steels with complex chemical composition and higher carbon contents. Under the conditions achieved during the LPBF process, such tool steels composition may lead to the presence of residual stresses within the part promoting cracks nucleation and propagation, thus making the part unusable. In this work, a low alloy tool steel AISI S2 with a medium carbon content (0.5 wt. %) was successfully processed by LPBF. As-built microstructure revealed fresh martensite, bainite and tempered martensite in a supersaturated condition, with the presence of residual stresses. In addition, phase transformations can occur in service at high temperature, affecting the mechanical properties of the part. Therefore, Differential Scanning Calorimetry (DSC) was performed on as-built samples to investigate the thermal behaviour of the material within the range 200 – 400 °C, with the aim to design a post-thermal treatment to stabilize the microstructure. Microstructural characterization was carried out on as-built and heat treated samples, in combination with macro- and nano-hardness analysis. Tribological tests were also carried out on as-built and heat treated samples. Wear properties were further assessed through observations of the worn track and counter-body surfaces and of transversal sections underneath the worn track.

ABSTRACT. In the process of actuator design, the limitations imposed by conventional manufacturing processes can be very restrictive. This is particularly true for certain types of actuators such as axial flux machines, where the lamination of the magnetic circuit, necessary to limit the occurrence of induced currents, is very complex. Additive manufacturing techniques, and in particular laser powder bed fusion (LPBF) of soft magnetic Fe-Si alloys, are likely to provide an answer to these limitations. To reach good magnetic properties, both in terms of magnetic permeability and iron losses, high silicon content Fe-based alloys have potential. However, at the desired contents, these alloys become very brittle, leading to numerous defects when used with LPBF, in particular the appearance of cracks and porosities. Babuska et al [1] showed that it is possible to enhance the ductility of Fe-50Co, and thus reduce the appearance of defects on brittle magnetic alloys, by regulating heat flows during the print. Inspired by their work, the present study aims to investigate how heat fluxes towards the building platform influence the formation of defect in the printed component. The effect of various support topologies is investigated by studying thermal dynamics using print-specific thermal curves. Dynamic finite element method (FEM) simulations are used to understand and manage heat fluxes. Finally, the validity of the thermal simulations is assessed by comparison with thermal measurements, and an evaluation is carried out on a complete print to reinforce the impact of heat flow management.

[1] Tomas F. Babuska et al., An additive manufacturing design approach to achieving high strength and ductility in traditionally brittle alloys via laser powder bed fusion, Additive Manufacturing, Volume 34, 2020, 101187, ISSN 2214-8604, https://doi.org/10.1016/j.addma.2020.101187

ABSTRACT. Structures made of pressurized membrane elements are gaining in popularity due to their numerous ecological qualities, including reusability, ease of repair, and minimal material usage. Such components are made from airtight coated fabric that acquire load-bearing capacity when filled with a pressurized gas. Although the majority of inflatable components exhibit curvature, such as inflatable cushions and beams, inflatable panels remain flat after inflation due to a large number of threads (known as "drop-stitch") that connect the two parallel flat sides. However, standard plate theories cannot capture their pressure-dependent behavior. In this work, inflatable panels are investigated analytically, numerically and experimentally. Nonlinear equations of motion are obtained from the principle of virtual power in coordinate-free notations. These equations take into account the shear effects through the Mindlin-Reissner kinematics as well as the inflation pressure dependency which tends to increase the overall stiffness. Solutions to the linearized equations are given for a circular panel with uniform vertical load. The analytical solutions are successfully compared to experimental results and to fully nonlinear simulations of the three-dimensional structure of the panel. Furthermore, the linearized eigenvalue problem is solved to obtain the natural frequencies and shapes for clamped, simply-supported and free edges. The successful derivation of the equations of motion now enables the study of buckling of inflatable panels, and the creation of a dedicated plate finite element. We anticipate that this work will facilitate the design and reliability analysis of inflatable buildings.

ABSTRACT. Most soft biological tissues are pressurized cellular solids. In plants, motion is performed by controlling pressure at the cellular level. An increase of the fluid pressure inside the elastic cell, that is called turgor pressure, creates cell expansion and deforms the tissue. This motion-by-deformation strategy occurs in almost all growing shoots but also in some mature plant actuators. For instance, Mimosa Pudica moves its leaves on demand by playing on turgor pressure gradients in pulvini.

Turgor pressure creates motion but it also changes the mechanical properties of pressurized cellular solids. We investigate the macroscopic (or apparent) mechanical properties of pressurized cellular solids considering a cell enclosing fluid. Several fluid behaviours (isobar, isochoric, adiabatic, isotherm and osmotic) and cell geometries (spheres or cubes) are considered as these play on apparent stiffness. This problem is written in terms of elastic and fluid energies. The second derivative of the total energy in a direction gives the elastic constant of the cell. This elastic constant is scaled by the volume of the cell after pressurization to obtain the apparent Young modulus.

The model shows that considering linear behaviour for solids, the effect of pressure on the apparent Young modulus is complex, and dependent on both cell relative thickness t/R and Poisson ratio. Considering mechanical properties of plant cells, the current model does not reproduce the pressure-induced stiffening of plant tissues observed in nature. We conclude that non-linear effects must be key in the observed stiffening in living tissues.

ABSTRACT. Turgor pressure (pressure inside cells) changes the rigidity of soft living tissues. For instance, the basil wilts when dehydrated or carrots soften when forgotten in the fridge. How does the stiffness of pressurized solids vary with turgor pressure and cell geometry? Current models of pressurized cellular solids show pressure-induced stiffening, regardless of the internal fluid behaviour. For a fixed volume, Nilsson (1958) showed that apparent Young modulus increases with turgor pressure. For a fixed pressure in shells, Vella et al. (2012) and more recently Couturier et al. (2022) also showed pressure-induced stiffening. Surprisingly, preliminary experiments on cubic cells showed pressure-induced softening of the cellular material. Both geometry and fluid behaviour seem to be key ingredients for mechanics of pressurized cellular solids. We tackle this problem experimentally considering a pressurized spherical membrane model enclosed between two parallel planes. Fluid behaviours considered experimentally are (1) isobar, (2) adiabatic and (3) isothermal. A finite element modelling is used to complement the experimental data with (4) isochoric behaviour. This finite element modelling also allows testing cubic cell mechanical response with well defined boundary conditions. Results show global stiffening following the Laplace coefficient of the thermodynamic transformation. Systematic tests are automatically performed on polymeric commercial membranes of radius R and Young modulus E (sport balls/Yoga balls). Dimensionless thickness, t/R, baro-elastic number P/E, and dimensionless indentation δ/R are considered to output the dimensionless force F/PR2. This work aims to understand the link between complex tissue architecture and tissue stiffness. Further steps are (1) mimicking living tissues to create mechanically tunable materials, (2) mimicking turgor induced motions and (3) the creation of resilient actuators.

ABSTRACT. Inflatables are particularly popular in the field of shape morphing materials. Their simple, purely mechanical actuation allows for fast deployment and high reusability. Moreover, just as the overall shape and stiffness of a party balloon are directly linked to its internal pressure, inflatable objects offer an elegant example of the coupling of elasticity and geometry.

We study networks of parallel inflatable tubes obtained through the planar welding of two plastic sheets. Composite tubes presenting two sides of distinct stiffness can be made by using two sheets of different thicknesses. Upon inflation of such tubes, a mismatch of curvature between the two walls rotates the seam line connecting them. Those local displacements allow for enormous deformations when integrated across large networks. We present experimental results on the mechanics of inflation of either one or several connected tubes.

The shapes of the tubes can be predicted throughout inflation using a simple Kirchhoff beam model, for which analytical solutions are determined for the limit cases of low and high pressures. In the latter case, a boundary layer at the edge of the seam line fully determines the rotation between two connected tubes. We highlight as well how contact between neighboring tubes limits in practice the overall motion of our inflatables.

Afterwards we formulate and solve an inverse problem to design a wide variety of objects that can be described as a two-dimensional curve perpendicularly to the direction of the tubes. The question of the stiffness of such structures is discussed as well. We finally present several applications of asymmetric tubular inflatables to more complex geometries: axisymmetric surfaces, kirigami, and curved folding.

ABSTRACT. A sheet of paper or plastic is difficult to stretch. However, by alternately cutting the sheet, it can be made macroscopically stretchable. What's the secret of this flexibility? Locally, the structure unfolds by bending, a low-energy deformation for a thin sheet. This kirigami technique is not limited to linear "garlands", it can be developed in both planar directions, resulting in three-dimensional structures. The final state depends on the geometry of the cuts. Can these cuts be programmed into the sheet to achieve the desired expanded shape? We've partially solved the problem for axisymmetric shapes, but what about an arbitrary target shape?

ABSTRACT. Poroelastic hydrogels display dissipative behavior due to liquid diffusion, and defining fracture toughness is an open issue. Our primary interest is fibrous gels such as cartilage, blood clots, and carbon-nanotube-based sponges with absorbed oils which suffer a reduction in volume by the expulsion of liquid under uniaxial tension, which directly affects crack-tip fields and energy release rates. We have carried out experiments on fibrin gels coupled with a large-deformation continuum model to investigate the initiation of crack growth. The continuum model is formulated for isotropic fibrous gels that exhibit a range of behaviors volume increasing to volume decreasing in uniaxial tension by changing the ratio of two material parameters. The direction of liquid fluxes around cracks is shown to depend on whether the gel locally increases or decreases in volume. The energy release rate for cracks is computed using a surface-independent integral and it is shown to have two contributions — one from the stresses in the solid network, and another from the flow of liquid. The contribution to the integral from liquid permeation tends to be negative when the gel exhibits volume decrease, which effectively is a crack shielding mechanism. Both from correlations with experiments and from simulations based on a critical stretch fracture criterion, we show that both contributions are required to characterize the fracture toughness of these materials. Some historical perspective on fracture toughness of dissipated solids will also be discussed.

ABSTRACT. Austenitic stainless steels are commonly used in industry due to their exceptional mechanical properties and corrosion resistance. However, intergranular fracture can occur in high-temperature aqueous environments, such as in Pressurized Water Nuclear Reactors (PWR). To model and predict stress corrosion cracking, it is necessary to estimate the fracture properties of oxidized grain boundaries, but experimental data is limited. This study assesses the fracture properties of a FeCr12Ni26Si3 austenitic stainless steel grain boundaries through a combined experimental and numerical approach. Micro-cantilever beams are milled at grain boundaries using Focused Ion Beam on samples oxidized in PWR environment up to 7470h. In-situ Scanning Electron Microscope bending tests are performed at room temperature, leading to brittle fracture either inside the intergranular oxide or at the metal/oxide interface. Preliminary estimates of critical stress and fracture energy can be obtained from experiments. However, for more accurate estimations, numerical modelling is required. Finite element numerical simulations, including cohesive zone modelling, are performed to predict micro-cantilever deformation and fracture. The critical stress (σc) and fracture energy (γc) are adjusted to reproduce the experimental data, resulting in σc = 1000 ± 250 MPa and γc = 11 ± 3 J.m-2. These values are in agreement with available experimental data for similar materials. Finite element simulations are finally used to assess the dependence of fracture properties and locations on experimental parameters, providing guidance for refined experimental assessment of grain boundary fracture properties.

ABSTRACT. Hydrogen-enhanced decohesion (HEDE) is one of the Hydrogen Embrittlement (HE) mechanisms and consists in the lowering of the atomic bond strength due to the trapping of dissolved hydrogen atoms at the crack surface of a material. In the last few years, phase-field methods have emerged as a powerful tool to describe such a phenomenon at the continuous scale. Usually, the reduction in the cohesion properties is modeled by explicitly decreasing the critical energy release rate, as a function of the hydrogen coverage.

In this work, to simulate the HEDE mechanism, we propose a new phase-field approach, based on the Kim-Kim-Suzuki (KKS) formalism, which is more rigorously connected to the segregation physics of the hydrogen atoms at the crack surface. This variational formulation accounts naturally for the decrease of the surface energy, in conjunction with the hydrogen atoms trapping, by minimization of the total free energy of the system. The present model and some validation tests are first presented, followed by a systematic study of the HEDE mechanism in Ni-based alloy. We investigate in particular the role on HE of pre-existing microstructural features like dislocations, grain boundaries, etc.

ABSTRACT. Certain metals, when exposed to a hydrogen environment---notably in hydrogen production, storage, and transport---experience a substantial deterioration in mechanical properties, an effect termed hydrogen embrittlement. To understand, predict, and counteract this hydrogen-assisted material degradation, sufficiently accurate material models are needed. According to the current hypothesis, hydrogen diffusion is driven by gradients of concentration and hydrostatic stress [1]. To capture this, a phase-field model is formulated as a multi-field problem coupling deformation, crack propagation, and diffusion to analyze hydrogen-promoted fracture. Here, the displacements, a fracture-related phase-field, the hydrogen lattice occupancy, and the chemical potential are considered as primary field variables. Approaches proposed in the literature often use an extrapolation of the hydrostatic stress calculated at the integration point level onto the nodes and later compute the gradient of hydrostatic stress [1]. This extrapolation process can introduce errors in the distribution of hydrostatic stresses throughout the material domain, potentially affecting the reliability of the simulation results. To address this, the model is reformulated into a mixed rate-type variational setting using a generalized Legendre transformation [2]. This introduces the chemical potential---whose gradient governs the hydrogen flux---as an additional variable dual to the hydrogen lattice occupancy. The primary field variables are obtained through the numerical solution of this saddle point problem. Moreover, the model's versatility in practical applications is enhanced by the ability to prescribe Dirichlet boundary conditions for the chemical potential and both homogeneous and inhomogeneous Neumann boundary conditions for the hydrogen flux on the specimen boundary. Furthermore, the inherent symmetry of the tangent moduli enables the use of symmetric solvers, and the flexibility of the framework easily accommodates additional fields of interest. Results for several representative boundary value problems are presented to demonstrate the applicability of the developed numerical framework.

[1] https://royalsocietypublishing.org/doi/10.1098/rspa.2013.0641 [2] https://doi.org/10.1016/j.jmps.2020.104093

ABSTRACT. During ductile tearing of ductile thin sheets, large plastic strains develop before failure. Numerically, plasticity is generally treated with macroscopic von Mises type plasticity but more complex plasticity effects may be at play affecting the tearing behavior. In this study, the effect of crystallographic texture and grain shape and size on the strain development during ductile tearing is assessed both experimentally and numerically for five different Al alloys sheets of one mm thickness [1,2,3]. Experimentally, in situ synchrotron imaging experiments are carried out to study the strain fields and damage development in the material ahead of the notch. Synchrotron laminography is used to image regions of interest in the aluminium sheets at micrometer resolution. Image correlation of projected 3D image contrast in the material bulk is used to identify the strain fields. For textured materials, strongly heterogeneous strain fields differing from the von Mises type model predictions are found whereas fine grained materials with little texture lead to strain field similar to those obtained by simulations using von Mises plasticity. Plane strain crystal-plasticity simulations are carried out to understand the experimentally found strain heterogeneity and allow the experimental trends to be reproduced [3]. Another phenomenon, leading to strain localization and instabilities during ductile tearing is the Portevin-le Chatelier (PLC) effect. The influence of the PLC effect on strain development for a 2XXX alloy and a C-Mn steel is studied using incremental surface image correlation thereby studying the experimental equivalent to strain rate [4].

[1] T.F. Morgeneyer, et al. Acta Materialia, 69 (2014) 78-91 [2] A. Buljacet al. Acta Materialia, 149 (2018) 29-45 [3] T. F. Morgeneyeret al. International Journal of Plasticity144 (2021) 103028 [4] S. Ren et al. International journal of plasticity 136 (2021) 102880

ABSTRACT. The 3D problem of out-of-plane perturbation of a semi-infinite plane crack, loaded arbitrarily in an infinite elastic body, was solved by Movchan et al. His method used analytical tools specifically adapted to the infinite geometry. In contrast, the same problem is solved here using a more general approach, relying on a recent extension of the author’s of Buekner-Rice’s theory. In its original form, this theory provided the first-order expression of the variation of displacement anywhere in the body, induced by a small tangential perturbation of the crack front (lying within the local tangent plane); in its extended form, it provides the same result but for a general perturbation of the crack front and surface, involving tangential and normal components. The variation of displacement is expressed as a sum of two integrals over the crack front and surface, respectively.

The extended theory is applied to Movchan’s problem in three steps :

(1) Letting the point of observation of the variation of displacement go to the crack surface, we first get the variation of the displacement discontinuity across this surface, anywhere on it. (2) We then use Bueckner-Rice’s original theory to get the displacement discontinuity anywhere on the unperturbed surface, induced by certain point loads – whose expression is required to apply the extended theory. (3) Applying the extended theory, we finally let the point of observation of the variation of the displacement discontinuity go to the crack front, to get the perturbed stress intensity factors there.

Although the derivation involves non-trivial evaluations of certain limits of integrals, it reduces the treatment to this purely mathematical task, circumventing the search of a method of solution of the full elasticity problem implied. This makes the method versatile and potentially applicable to other cracked geometries, closer to those of actual fracture experiments.

ABSTRACT. Objective of this work is to identify potential safety issues related to uncontained engine installation and to evaluate the impact on aircraft design. A careful assessment of the certification specifications relating to propeller installation is therefore carried out. To identify the safety issues, it is required to do an analysis to evaluate the area and danger of propeller debris impact.

The results of this analysis will be used to identify modifications to the aircraft design and to evaluate the weight increase due to debris shielding addition. New materials (composite, hybrid) are considered in shielding application vs a fuselage made out of aluminium. A summary presentation of the most promising material is presented to see/conclude on the utility of them for the reinforcement of structures submitted to high impact as blade release with high energy. Each material is regarding: potential for the shielding function, the manufacturability, the expected development effort regarding design, the simulation possibilities and the feasibility/viability of the concept. Thus, an approach with added patches on conventional structure seems to be the best compromise regarding mass, cost, manufacturing and integration aspect. Numerical simulations [10] based on a mesoscopic approach (modelling of plies and potentially delaminating interfaces) provide a detailed analysis of the consequences of a high-speed impact on a shielding-type material. However, they remain too costly for a shielding evaluation study.

This is why ONERA has decided to develop the following computational strategy: - A numerical homogenization approach is used to represent any type of potential shielding material, and more particularly shielding with laminates or woven architectures that could be found in patch form. - An optimization strategy to determine the required mechanical properties and orientation of plies and woven to absorb the impact energy providing from a blade release. A strategy of optimization is presented for shielding evaluation.

ABSTRACT. Wrinkles can be found on the surface of largely compressed areas of metallic materials. These surface instabilities can be observed in structural elements that are of interest for the automotive and offshore industries, such as bent tubes or pipes, pressure vessels or die formed sheet metal pieces. Wrinkles are understood as undulations or surface roughness that might set in due to large straining in metallic materials. Typically, they present distinct geometrical features that are periodically repeated on the surface and they are dimension-wise significantly smaller than any of the dimensions that define the rest of the solid. They fold and self-contact, creating surface defects when the structural elements are increasingly compressed, and may lead to a ductile-to-brittle transition if subsequently strained in tension. Eventually, the self-contact grows unsteadily evolving into a crease, a specific type of singularity.

To analyse such an effect, a finite element model of a half-space plane-strain material block with an imperfection was subjected to different levels of compression followed by reverse tensile straining. The existence of a critical strain, for which the self-contact defect acted as a crack during the tensile straining phase predicted by the model was confirmed by reverse compression-tension tests performed at two different strain rates. A post-mortem fractographic analysis allowed to link the ductile-to-brittle transition strain to the morphology of the fracture surfaces. This experimental analysis demonstrated that the findings from the numerical simulations using strain localisation theory were in line with the experimental results.

ABSTRACT. Easy open ends (EOE) play a pivotal role in food can packaging, where efficient material utilisation through shell thickness reduction not only brings economic benefits but also contributes to ecological sustainability. The EOE components, the tab and the end, are independently manufactured and then riveted together. The V-shape score line featured in the latter, represents the weakest part of the assembly, necessitating special attention. The structural integrity and functionality of both components is crucial for ensuring the optimal performance during the can manufacturing and performance process. To address this, materials commonly used in the food packaging industry families were selected: i) two steels grades, TH550 (tab) and ML460 (end) and ii) two aluminium alloys 5182-H48 (tab) and 3104-H26 (end). Their elastoplastic properties were characterised and represented with Hill-48 plasticity and combined Swift-Vode hardening models for the FEM forming analysis. To ensure the material’s performance robustness during the forming operation, the Hosford-Coulomb ductile fracture initiation criterion’s properties were also calibrated for the as-received materials. for the sake of simplicity, the score line was treated as an independent virtual material with continuous thickness properties. The score geometrical feature was removed and instead represented by the said material maintaining a reasonable mesh size throughout the whole component. Finally, experimental performance tests were conducted to assess the validity of the FEMs, showing good agreement.

ABSTRACT. Using TBI-on-a-chip integrated with computational modeling, we have established a map of differential forces on the network adhered-MEA “chip” using finite element analysis. We found that while impacts induced an overall loss of dendritic spines, with the remaining spines revealing increased levels of mislocalized tau coupled with acrolein, such changes are not uniform. Specifically, these impact-induced changes are significantly intensified at the “edges” of the MEA, where we calculate the force to be higher (relative to the lower-forces experienced at the MEA “center”). Interestingly, acrolein exposure alone in the absence of impact is capable of partially mirroring all of these impact-induced phenomena. In addition to mechanical and biochemical investigations, we also show that impact, in a dose dependent fashion, causes a reduction of activity (spike rate), a functional deficit that can also be mimicked using acrolein. Further, we also show that impacts not only reduce activity, but also suppress, on average, the synchronization of the brain electrical activity, which again, can be partially recreated via acrolein exposure. These results reveal the quantitative relationship between mechanical forces and resulting biochemical, structural, and functional injuries, in the TBI-on-a-chip model, with greater spatial and temporal resolution then previously possible. Finally, this study, along with several previous reports utilizing TBI-on-a-chip, continue to implicate acrolein as a key culprit in post-TBI AD, suggesting that acrolein could provide a promising therapeutic target for slowing or even preventing the progression of TBI to AD.

ABSTRACT. The fetal head is comprised of bony plates joined together by soft connective tissue, known as sutures. During the second stage of labour, the fetus is expelled from the uterus through the birth canal. Sutures allow the fetal head to mould whilst in the birth canal, which, due to the constraints of the maternal anatomy, significantly aides the descent of the fetus. However, moulding of the fetal cranium also causes moulding of the fetal brain. Excessive moulding can result in brain trauma and other long-term sequelae for the fetus. Therefore, understanding the loading experienced by the fetus during labour could help elucidate the risk and mechanism of injuries, and conversely helping predict the safety of the newborn during vaginal delivery. This study proposes a computational model comprised of the fetal head and maternal labour environment capable of predicting the stresses and deformations experienced by the fetal brain during the second stage of labour. The finite element model was adapted from existing studies to represent the geometry of full-term pregnancy. Different model metrics were varied and then compared based on their effect on labour, the results of which will be discussed in this presentation.

ABSTRACT. White matter (WM) tract-related strains have been increasingly used to quantify brain responses, but its dynamics under the live, human brain during non-injurious impact conditions remain largely unknown. Recently, one in-vivo study measured the normal strain along the WM fiber tracts (i.e., tract-oriented strain), but it only represents a partial description of the fiber deformation. We aim to extend the measurement of WM deformation by quantifying the normal strain perpendicular to the fiber tracts (i.e., tract-perpendicular strain) and the shear strain along and perpendicular to the fiber tracts (i.e., axial shear strain and lateral shear strain, respectively) under voluntary neck rotation and neck extension. To achieve this, we combined the three-dimensional strain tensor from the tagged magnetic resonance imaging with the diffuse tensor imaging (DTI) from an open-access dataset, including 41 subjects under neck rotation (n = 27) and neck extension (n = 14). The strain tensor was rotated to the coordinate system with one axis aligned with the DTI-revealed fiber orientation, through which three tract-related strains were extracted. The results showed that the strain peak is dependent on the loading mode (p<0.05, Mann-Whitney U test). Under neck rotation, the peak values ranged from 0.012 ~ 0.042 for tract-perpendicular strain, 0.010 ~ 0.035 for axial-shear strain, and 0.010 ~ 0.035 for lateral-shear strain. Under neck extension, the maximum values varied from 0.012 ~ 0.024 for tract-perpendicular strain, 0.010 ~ 0.020 for axial-shear strain, and 0.011 ~ 0.022 for lateral-shear strain. The strain distribution is dependent on both the strain modality and loading mode. Our study presented the first in-vivo analysis of tract-perpendicular strain, axial-shear strain, and lateral-shear strain towards an improved understanding of WM dynamics. The reported strain results can be used to evaluate the reliability of computational head models, especially those intended to predict brain strains under non-injurious conditions.

ABSTRACT. Stroke is a leading cause of death worldwide, with approximately 3 million deaths in 2022. This study investigates the effect of calcium content on embolus analog (EA) mechanical properties as an indication of EA behavior in time dependent, high strain load states such as mechanical and aspiration thrombectomy.

Human blood was collected from healthy donors, anticoagulated, separated via centrifugation, and controlled for platelet count and hematocrit. Blood was recalcified in a Chandler loop and allowed to coagulate at 37C for 1 hour. EAs were then placed in 0 (Dulbecco’s Modified Eagle Media), 0.2 M calcium chloride, and 2 M calcium chloride baths for 1 and 10 days with control clots tested on day 0. Cylindrical specimens were loaded onto an Instron (Natick, MA, USA) uniaxial load frame to perform a high-strain relaxation test. Tangent stiffnesses at 10 and 75% strain, percent relaxation, and clot area were recorded, and a histological analysis was used to visualize clot structure. Statistical analyses were performed in MATLAB.

Peak stress and tangent moduli were significantly higher, and percent relaxation was lower for days 1 and 10, 2 M calcium EAs, while clot diameter did not change significantly over the aging and calcification period. Preliminary histological analysis reveals a decrease in red blood cell percentage for all aged clots. Significant changes in aged and calcified clot properties and decrease in clot viscous relaxation behavior suggests that calcification may increase the risk of thrombectomy complications because of increased clot stiffness, a factor directly affecting surgical outcomes.

ABSTRACT. Paediatric hydrocephalus is a serious medical condition characterised by an excess of cerebrospinal fluid (CSF) in the lateral ventricles of the brain. CSF is produced by the Choroid Plexus (CP) tissue, a vascularised fin-like structure rooted to the bottom of the ventricles. A common treatment for congenital paediatric hydrocephalus is the insertion of a shunt system containing a ventricular catheter, a hollow tube with inlet holes arranged in the tube wall close to the closed tip. Shunt systems run the risk of the CP occluding the catheter holes during drainage, causing it to block and require replacement. Replacement surgery has the added risk of haemorrhage if the entwined CP tears when the blocked catheter is removed. While various catheter geometries have been proposed over the last 50 years to minimise blockage risk, there is no clear evidence of the relative efficacy of different designs. We present a computational fluid-structure interaction (FSI) model combining open-source OpenFOAM with in-house software MuPhiSim, which simulates the deformation of the CP in an idealised ventricle-catheter environment. The resulting FSI model provides a framework to test the efficacy of different catheter designs, with two catheters currently in use in clinical settings being compared. A reduction of the model to 2D – computationally far more efficient – is used for parameter sweeps over hole size and position. The results are then used to motivate candidates for new 3D designs. These geometries are simulated in the full FSI environment and shown to be an improvement on existing designs.

ABSTRACT. A model for description of the multi-axial creep response of single crystals is presented. An over-stress type approach in conjunction with an yield criterion that accounts for the intrinsic crystal symmetries is adopted. The creep stabilization is considered to be governed by the irreversible work per unit volume. The influence of anisotropy, namely crystallographic orientation and loading path history on the creep response is analyzed in detail. We conclude with discussion of possible extensions of the model such as to account for viscoplasticy-damage couplings.

ABSTRACT. Fibrous materials, such as mineral wools, can be used for acoustic insulation in different building elements (partition walls, ceilings...). Mineral wools are porous random sparsely linked fibre networks, whose microstructure must be studied to improve their acoustic behaviour. In the past, macroscopic acoustic parameters have been linked to microstructure, based on the hypothesis of rigid fibrous skeleton. This hypothesis appears to be inaccurate to model certain applications, such as floating floor or partition walls, when the structure displacement must be considered. The main goal of this paper is to study the dynamic behaviour of mineral wool, as well as to establish a link between microstructure and macroscopic mechanical properties. Confocal microscope images, and micro-scale observations allowed to identify some characteristics of the material. Preliminary experiments confirmed that it is strongly anisotropic, even at small scales. The through-thickness compression stiffness is relatively low, whereas in the transverse direction fibre naps are identified. Macro-scale measurements of dynamic quantities of interest (stiffness, loss factor) were performed on a batch of samples of different properties. Results showed the influence of the different process/micro-scale parameters on the dynamic behaviour of the material. A Finite Element Method numerical model of a microscale 3D Representative Volume Element (RVE) of a Non-Uniform Rational B-Splines (NURBS) fibres geometrical network is being developed based on the micro-scale observations. The originality of this model lies in description of the three-dimensional small strain dynamic behaviour of a sparsely cross-linked network. Especially, it is necessary to better understand various phenomena, such as contact, friction, or binder influence. A specific modelling strategy is proposed to model the binder links between fibres. Results of the FEM model are compared with macro-scale acoustic measurements. To be able to link model and experiments, a key issue is to identify the scale of the model.

ABSTRACT. Open-porous cellular solids are lightweight structures with ultra-low bulk densities and thermal conductivity, high structural stiffness and energy absorption capacity. In this study, a computational method is developed to model open-porous microstructures and predict their relevant elastic and inelastic mechanical properties, as well as the thermal conductivity. First, the geometry of the microstructure is generated for a given pore size distribution (PSD) and porosity. To this end, the Laguerre-Voronoi tessellation and close sphere packing are applied. This allows us to reproduce highly irregular cell shapes and sizes relevant for biopolymer aerogels considered in this study for a benchmark example. The PSD of the resulting geometry is validated in comparison with the experimental data obtained from nitrogen desorption isotherms and further exported as beam elements to the finite element (FE) model. FE simulations of a representative volume element further allow to evaluate the homogenized mechanical response of the porous structure based on its micromechanics and to study its heat transfer properties. Finally, the influence of PSD and porosity on the mechanical and thermal properties is discussed.

ABSTRACT. Accurate predictions of ductility limits play a crucial role in product design and manufacturing, offering substantial cost reductions in development. In this investigation, attention is focused on the prediction of ductility limits for porous materials. Unlike previous contributions [1,2], we integrate a microscopic damage model based on thermodynamics into the crystal plasticity finite element method (CPFEM) framework in the current study. In this regard, Representative Volume Elements (RVEs) are selected to represent the porous materials at the macroscopic level and an ABAQUS Voronoi Toolbox is developed to generate these RVEs. The macroscopic behavior of these RVEs is determined from that of the constituent single crystals using the periodic homogenization multiscale scheme [1,2,3]. At the single crystal scale, the constitutive equations follow a finite strain rate-independent framework, where the damage variables are defined for each individual slip system. The plastic flow rule is governed by the classical Schmid law. The proposed model is applied to predict the ductility limits for porous materials using the Rice bifurcation criterion. The results show that the damage coupled CPFEM approach accurately predicts the ductility limits, offering valuable tools for optimizing the mechanical properties of advanced materials. REFERENCES [1] Zhu JC, Ben Bettaieb M, Zhou S, Abed-Meraim F. Ductility limit prediction for polycrystalline aggregates using a CPFEM-based multiscale framework. Int J Plast 2023;167:103671. [2] Zhu JC, Ben Bettaieb M, Abed-Meraim F, Huang MS, Li ZH. Coupled effects of crystallographic orientation and void shape on ductile failure initiation using a CPFE framework. Eng Fract Mech 2023;280:1–21. [3] Miehe C, Schröder J, Schotte J. Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput Methods Appl Mech Eng 1999;171:387–418.

ABSTRACT. Soft granular materials, consisting of highly deformable disordered particles, find applications in various industrial sectors such as pharmaceuticals, cosmetics, food, and powder metallurgy. These materials are often shaped under confinement stresses in processes like extrusion or compaction, resulting in tablets or compacts with a microstructure resembling that of porous media. The compaction stage remains challenging to describe, marked by changes in particle shape, volume, and rearrangements within the grain bed. In this context, suitable numerical models are necessary to capture the significant deformations of particles at the contact level. An important challenge lies in ensuring the representativity of simulated systems for industrial applications. The number of simulated particles relative to the system size is a key parameter. In tis presentation we will focus specifically on the finite size effects of systems composed of slightly polydisperse elastic spherical particles confined within rigid cylinders of varying diameters. These particles will undergo quasi-static uniaxial compression with a home-made code relying on couple approaches based both on material point method for bulk particle deformations and contact dynamics method to address particle-particle interactions. The diameter and height of the cylinders will be vary based on the number of particles, allowing us to elucidate how the number of particle influences important packing parameters such as stress transmission, solid fraction, or connectivity.

ABSTRACT. In the realm of material science, the development of gradient-enhanced plasticity theories has marked a significant advance in modeling small-scale phenomena. These theories can effectively capture the size-dependent behavior of materials at small scales, where traditional plasticity approaches are often inadequate. A key focus of recent research is the accurate modeling of higher-order effects using such advanced theories. Despite ongoing debates, there is a consensus among researchers about the necessity of considering both energetic and dissipative higher-order effects to enhance the accuracy of these theories. To this end, two main decomposition methodologies have been proposed: higher-order stress decomposition (parallel approach) and higher-order kinematic decomposition (series approach) into recoverable (energetic) and unrecoverable (dissipative) parts. The present contribution aims at providing a comparative study of these two methodologies, within strain gradient crystal plasticity (SGCP) framework. Their capabilities to deal with elastic gaps under non-proportional loading conditions are also investigated. Findings of this work highlight the effectiveness of the higher-order kinematic decomposition approach. This approach has shown promise in avoiding elastic gaps, and the associated results are qualitatively in good agreement with those obtained using discrete dislocation dynamics (DDD). This suggests that this decomposition approach may be more accurate and reliable for modeling small-scale material behaviors by gradient-enhanced continuum theories.

ABSTRACT. The notion of elastic incompatibilities considers elastic deformations from one configuration to another. In this contribution, elastically anisotropic materials are discussed within the context of a large-deformation Eulerian formulation that is free from arbitrary choices of reference and intermediate configurations as well as definitions of total and plastic deformations. Specifically, the assumed formulation holds for elastically anisotropic materials, as it relies on evolution equations for a right-handed triad of linearly independent microstructural vectors. In particular, these evolution equations involve the plastic rate second-order tensor, which requires a constitutive prescription. The microstructural vectors are internal state variables since they are assumed to be measurable in the current state. They describe elastic deformations and orientation changes of material directions relative to a zero-stress state, so that they also determine the Cauchy stress in the current configuration. Hence, an elastic deformation is defined from an arbitrary initial configuration that can have a state with elastic incompatibilities. Necessary and sufficient conditions are obtained for additional elastic incompatibilities developing from this initial configuration. Moreover, a second-order Eulerian tensor is proposed, based on the current curl of the plastic rate tensor, which measures the current rate of incompatibility. If restricted to small strains and rotations, this incompatbility tensor is the opposite of the rate of the Nye-Kroner dislocation density tensor; therefore, the diagonal and off-diagonal components of the proposed incompatibility tensor correspond to screw and edge dislocation density rates, respectively. A hardening law dependent on the this incompatbility tensor is developed to study size-effects in small-scale metal plasticity. In order to unveil the features of the proposed theory, the large-deformation torsion of a cylinder is analyzed for both monotonic and cyclic loadings.

ABSTRACT. In this talk, we will discuss one-dimensional strain-gradient theory for special Cosserat rods. A general framework for micro- and nano-scale rods that accounts for large deformations, chirality, and size effects has been developed. Firstly, the linear momentum and angular momentum balance equations for rods have been derived using the three-dimensional strain-gradient elasticity theory. Additionally, the constitutive relations for the strain-gradient elastic rods have been derived using the principle of material objectivity. Subsequently, these constitutive relations have been used to show the applicability of the current theory by deducing the various closed-form solutions for geometrically nonlinear thin strain-gradient rods subjected to extension and bending deformations (like Elastica). Finally, we discuss the role of the length scale parameter on all these deformations of the strain-gradient elastic special Cosserat rod.

ABSTRACT. The work presents generalized (size-dependent) continuum mechanics, namely the space-fractional continuum mechanics, whose applicability is extended to problems with smaller characteristic lengths. This approach uses fractional calculus to account for information on the internal characteristic length of the microstructure and avoid the need to represent the complex original microstructure one-to-one. Fractional operators, as being defined on a specific interval, allow accounting for nonlocality, which should be understood that the current response of the model at a specific material point depends on information from its finite neighborhood.

The talk will focus on modelling the structural elements (beams and plates) defined in the framework of the aforementioned space-fractional continuum mechanics, which allows analysis over various scales (nano-micro-macro). The possibility of identifying damage in the structures at the nano/micro scale will also be addressed. Moreover, validation results lead us to the recognition that space-fractional continuum mechanics is an up-and-coming technique for modeling material bodies whose dimensions are of the order of the internal microstructure.

ACKNOWLEDGEMENTS This research was funded in part by the National Science Centre, Poland, grant number 2022/45/N/ST8/02421. For the purpose of Open Access, the authors have applied a CC-BY public copyright license to any Author Accepted Manuscript (AAM) version arising from this submission.

REFERENCES W.Sumelka, T.Blaszczyk. Fractional continua for linear elasticity. Archives of Mechanics, 66:147-172,2014. P.Stempin, W.Sumelka. Space-fractional Euler-Bernoulli beam model - Theory and identification for silver nanobeam bending. International Journal of Mechanical Sciences, 186:105902,2020. P.Stempin, W.Sumelka. Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects. Computational Mechanics, 68:697-708,2021. P.Stempin, W.Sumelka. Space-fractional small-strain plasticity model for microbeams including grain size effect. International Journal of Engineering Science, 175:103672,2022. P.Stempin, T.P.Pawlak, W.Sumelka. Formulation of non-local space-fractional plate model and validation for composite micro-plates. International Journal of Engineering Science, 192:103932,2023.

ABSTRACT. A nonlocal higher-order shear deformation beam theory is developed for bending of nanobeams based on the stress-driven model. Several distributions of the transverse shear strains are considered satisfying the zero traction boundary conditions on the surfaces of the beam. The higher-order shear deformation beam theories and the stress-driven nonlocal model provide the equations of nonlocal elastic equilibrium. Hence, it is shown that the stress-driven model is well-posed for higher-order shear deformation theories. The accuracy of the present approach is verified by comparing the obtained results with existing solutions.

ABSTRACT. As illustrated in a recent paper (Comput. Meth. Appl. Mech. Eng. 417A, 116399, 2023), the distance based data-driven paradigm for computational mechanics, labelled DDCM, can be revisited in the context of Game Theory. The classical DDCM formulation appears as a collaborative game, while an alternative adversarial game approach can also be derived. The latter approach offers the advantage to uncouple the data-driven constitutive description from the boundary-value field problem, allowing for easy integration in standard FE codes for example, at least in explicit dynamics or using matrix-free solvers.

We will illustrate how DDCM can be used in the context of computational multiscale mechanics of materials, both in its classical and in its game theoretical formulations. One important advantage of DDCM in the context of two-scale concurrent analysis lies in its capacity to efficiently reuse previously computed material response at the microscale (e.g. on a representative volume element), reducing the computational cost and leading to a goal-oriented sampling of the macroscopic material response.

ABSTRACT. According to the current understanding of fused deposition modelling (FDM), a typical extrusion-based 3D printing technology, it is expected that the stronger component can be achieved with the higher infill density. However, due to the complexity of the cross-correlations between multiple processing parameters, the prediction of mechanical strength of printed parts can be highly inaccurate. Therefore, considering the large variety of possible combinations of these parameters, the evident level of non-linearity between them and the mechanical strength has become the main problem to be solved.

The present research includes the application and evaluation of alternative data-driven methodologies, with development of prediction frameworks: dependent on the user needs, “direct” and “inverse” schemes. The former can be used to estimate mechanical strength with known processing parameters, whereas the latter can help identify the optimal combination of processing parameters that ensures the required mechanical strength. Note that the estimated processing parameters from the inverse framework must be adjusted with respect to specifications of the printer and the software.

In this investigation, three various data-driven methodologies were adopted and evaluated regarding their accuracy and efficiency, including the fuzzy inference system (FIS), artificial neural network (NN) and adaptive neural fuzzy inference system (ANFIS). The research has confirmed that with the priority being accuracy, the ANFIS is seen to be the most accurate approach, which requires particular computing power; however, FIS is reported to be the most efficient approach.

The intrinsic versatility of the analysed data-driven methodologies has proven that these approaches can be adopted not only for process and geometrical design parameters, but also for cost-relevant parameters such as printing time and material consumption. It is shown that data-driven methodologies can be an effective and robust decision-making tool in design and cost management problems.

ABSTRACT. Soft materials such as biological tissues or magnetorheological elastomers present complex mechanical behaviors that include large deformations, numerous nonlinearities, time- or even external field (magnetic)-dependent responses. The description of their constitutive modelling is challenging and often time-consuming. Numerical algorithms to automatically calibrate model parameters have provided invaluable tools to help this purpose. However, these are mostly limited to the fitting of a set of pre-defined parameters associated with the model used. In this work, we go a step further by developing a machine learning framework capable of automatically identifying not only such model parameters but also the optimal kinematics and rheological model. To this end, we present a multiphysics model-driven framework that optimally selects the most suitable model kinematics, its rheological components and their arrangement for a given set of experimental curves. Subsequently, it calibrates all the material constants belonging to such a model, independent of its complexity. We demonstrate the versatility and capabilities of this framework with examples on hyperelastic, viscohyperelastic and magneto-viscohyperelastic materials. The present work opens new routes to not only fit model parameters but to identify the constitutive ingredients and underlying mechanisms needed to describe nonlinear responses of soft active materials.

ABSTRACT. Rubber like materials demonstrate pronounce softening under cyclic loading. This phenomenon known as Mullins effect plays an important role in the stress strain response of these materials. Despite long-term research and numerous modeling approaches proposed in literature an accurate prediction of the Mullins effect especially under complex loading conditions still remains a challenging task. In this work, we propose a novel approach to model the Mullins effect using deep symbolic regression. The goal is to find a strain energy in the form of an algebraic expression fitting the given data as closely as possible. By incorporating deep symbolic regression into the continuum mechanical framework the method combines advantages of known physical relationships with the unbiased optimization approach of symbolic regression. The procedure has already been applied to discover incompressible hyperelastic material models and will be extended here to inelastic effects as well. The proposed approach is validated through benchmark tests using the generalized Mooney Rivlin and the Ogden Roxburgh model. In addition, the proposed framework is tested on an experimental temperature dependent data set. Good agreement between the obtained material models and the experimental data is demonstrated.

ABSTRACT. Low adhesion zones resulting from rail-wheel contamination, often associated with leaves, pose significant danger to train operation during autumn months, extending braking distances and leading to potential station overruns. While a range of mitigations exist, they often come with significant drawbacks. Due to this, there is appreciable motivation to predict problematic areas of low adhesion before they form, based on the location characteristics such as tree species and density near the track. Accurate predictions would help to direct mitigation work and address underlying conditions, reducing the number of affected areas, and so improving passenger safety. A new technique has been employed, allowing consideration of multiple complex parameters. Field data was applied to a novel fuzzy inference model, which been shown to be successful at generating adhesion delay predictions. The model was trained and validated, demonstrating excellent performance of the fuzzy method (less than 8% error). Through conducting a sensitivity analysis, it has been found that the density of trees and their distance from the track as well as the presence of problematic species play a significant role in producing low adhesion zones. Meanwhile, factors such as the overhang of trees or if the track is in a rural or urban area have been shown to have small influence on leaf layer buildup. The effectiveness of the model has been demonstrated for prediction of low adhesion zones and the methodology is ready to be further validated, moving towards operational application.

ABSTRACT. This research presents a new development in Equivalent Single Layer (ESL) plate theory, which utilizes the Variational Asymptotic Method (VAM) approach. ESL plate theories are mathematical models used to analyze the behavior of thin or moderately thick plates. They simplify the analysis by assuming that the plate is composed of a single layer, with constant properties throughout its thickness. While previous ESL plate theories exist, the majority of available models are axiomatic-based and assume displacement in the thickness direction. In contrast, VAM-based asymptotically correct plate models do not make assumptions a priori and are more mathematically rigorous. However, these models contain higher-order derivatives of the generalized strains and/or displacements, making the analysis complex and inefficient. Thus, it is necessary to eliminate them.

This paper makes two contributions to the literature. First, it focuses on achieving maximum accuracy to the strains for a particular computational cost, rather than for the displacement field. As a result, the proposed model provides strains that cannot be obtained by considering any assumed form of displacement along the thickness direction. This approach results in a better representation of the energy of deformation of a plate. Second, the paper introduces a novel isoenergetic approach to eliminate the higher-order derivatives of the generalized strains present in the asymptotically correct plate model, while maintaining simplicity and accuracy

ABSTRACT. It is well established that the failure of rail steels originates in plastic strain accumulation, however the cyclic nature of simulating the phenomena is inherently slow. Recent advances in parallel computing for simulations have facilitated the remapping of a previously computationally limited model of the material response of rail steels under repeated rolling contact. A parallel computing framework using Nvidia graphics processing units (GPUs) has allowed for the introduction of new materials behaviour and expanded the scope for future work.

The dynamic ratchetting (Dynarat) model, developed in 2001, discretises a section of rail into a grid of elements called ‘bricks’, each of which are characterised by material properties such as shear yield and critical shear strain. Bricks accumulate strain in a ratcheting process with varying rates according to the maximum shear stress they experience, and the work hardening behaviour of the material. A brick is considered to have failed once the limit of critical shear strain is exceeded, which represents the formation of voids or cracks in the material. Originally used to model wear and microcrack behaviour in rail steels, lack of strain continuity between bricks and limited scale were deficiencies of the model that could not be addressed previously. However, the FLAME GPU framework, Flexible Large-scale Agent Modelling Environment for Graphics Processing Units, has allowed for the expansion of the model dimensionally, and for the addition of bonds between bricks to address continuity issues.

The paper documents the translation of the existing mechanics of materials model to an agent-based parallel simulation, facilitated by the GPU accelerated framework FLAME GPU. A study is reported here on how modelling speed is determined by factors including agent communication strategy. Enabled by the accelerated model, this also includes the addition of material bonds to improve the continuity and behaviour of the model.

ABSTRACT. Incoloy 800H is an austenitic Fe-Ni-Cr alloy whose creep behaviour is characterized by the onset of two minima within the creep strain rate-time curve. The underlaying physical phenomena inducing this mechanical response are still unclear. (Guttmann and Bürgel, 1983) attribute the first creep rate minimum to a creep mechanism transition induced by dislocation-pinning, whereas the second one is said to be consequence of internal nitridation. The creep hardening effect of nitridation in 800H is evidenced in (Young et al., 2023). Meanwhile, studies on austenitic steels exhibiting similar creep responses attribute both creep rate minima to two separate precipitate strengthening phenomena (Hatakeyama et al., 2022). it is thereby clear that the accurate prediction of the creep behaviour in 800H alloy requires the assessment of creep micromechanics and microstructure evolution. In this work, we provide a numerical framework for the implementation of a mean-field creep model adapted to predict the high-temperature creep deformation response of Incoloy 800H. As a semi-physical model, microstructure evolution is considered in the form of dislocation density distributions, average grain and sub-grain size, and primary precipitate kinetics. The latter is calculated separately via thermodynamic simulations. This approach has proved high accuracy for the prediction of dislocation-based creep deformation of P91 steel (Riedlsperger et al., 2020), and diffusion + dislocation creep deformation observed in A617 Ni-alloy (Riedlsperger et al., 2023). To predict the creep deformation response of 800H alloy, we adapt the model to consider all primary precipitates known to play a role in its creep behaviour (namely MC, M23C6 and TiN). On the basis of the work of (Young et al., 2023), further discussion is given on the possibility of the extension of the model to account for the internal nitridation of the alloy by including the precipitate kinetics of chromium (CrN, Cr2N) and aluminium (AlN) nitrides.

ABSTRACT. Crystal Plasticity formulations based on dislocation density field concepts incorporate a transport term in the evolutionary behavior of the dislocation densities. They consist of coupled, nonlinear differential equations that describe diffusive and convective transport mechanisms. Due to the hyperbolic nature of the dislocation density transport equations, the standard Galerkin finite element method results in spurious numerical oscillations and thus is unsuitable for achieving a stable numerical. Amongst the numerical problems used to address such dislocation density transport phenomena is the so-called upwind method. However, its use in solving highly nonlinear hyperbolic equations typical of those of interest in dislocation density field-based crystal plasticity formulations can result in slow convergence of the numerical solutions. In this work, it will be shown that it is possible to achieve higher numerical stability and efficiency by implementing the discontinuous Galerkin method. Several classical boundary value problems involving dislocation pile-up and the simple shear deformation of a constrained single crystal strip are carried out. A comparison of the computational efficiency of the upwind and discontinuous Galerkin methods is also discussed.

ABSTRACT. With the development of modern technology and materials, the expectations of customers and users regarding the broadly defined comfort of office and residential spaces are increasing. One of the more innovative solutions to provide better thermal comfort for users is diffuse ceiling ventilation. Due to its numerous advantages mainly associated with the elimination of local draughts and high cooling capacity, it is gradually gaining popularity, replacing traditional systems based on a series of pipes and point air outlets.

Therefore, interior architects are faced with the challenge of designing raster ceilings in such a way that profits from the use of diffuse ventilation can be maximised, while maintaining an aesthetically pleasing appearance. Increasingly, bionic inspiration is being used for this purpose, so that people in rooms designed with reference to natural patterns can work and live in a friendlier atmosphere.

The aim of this study is to model bionic-inspired raster ceiling tiles and analyse the airflow through various geometries of these tiles, differing in size, shape, and distribution of openings. Thanks to extensive numerical analyses, it was possible to draw general conclusions, determine certain geometrical parameters of the analysed tiles and their influence on pressure distribution and airflow velocity. The entire work is illustrated by graphs, histograms, and maps of distribution of the airflow parameters, which will make it possible in the future to design optimised bionic-inspired raster ceilings over entire rooms, thus enabling the most profitable use of diffuse ceiling ventilation, better thermal comfort of users and unique aesthetic experience.

ABSTRACT. With the development of modern technology and materials, the expectations of customers and users regarding the broadly defined comfort of office and residential spaces are increasing. One of the more innovative solutions to provide better thermal comfort for users is diffuse ceiling ventilation. Due to its numerous advantages mainly associated with the elimination of local draughts and high cooling capacity, it is gradually gaining popularity, replacing traditional systems based on a series of pipes and point air outlets.

Therefore, interior architects are faced with the challenge of designing raster ceilings in such a way that profits from the use of diffuse ventilation can be maximised, while maintaining an aesthetically pleasing appearance.  Increasingly, bionic inspiration is being used for this purpose, so that people in rooms designed with reference to natural patterns can work and live in a friendlier atmosphere. The aim of this study is to model bionic-inspired raster ceiling tiles and analyse the vibration induced various sources: fans, ventilator and impact hammer . Openings in raster ceiling tiles have different size, shape, and distribution of openings. Also raster ceiling tiles are composed from different materials steel, aluminium, mycelium base composite (MBC) and bamboo base composite. Obtained experimental results have been compared with numerical results from ABAQUS programme.

The entire work is illustrated by graphs, which will make it possible in the future to design optimised bionic-inspired raster ceilings over entire rooms, thus enabling the most profitable use of diffuse ceiling ventilation without problems with unwanted vibrations for better thermal comfort of users and unique aesthetic experience.

ABSTRACT. Raster ceilings are widely used in office spaces and residential buildings. Their application may involve the use of ventilation – both distributed and traditional – located in the space above the suspended ceiling. Both types of ventilation generate vibrations that are oppressive to users, which in case of inappropriate use of the ceiling tiles materials, may be additionally amplified by the phenomenon of resonance. Therefore, the issue of awareness of the dynamic properties of ceiling panels becomes extremely important. Due to this knowledge, it will be possible to avoid the occurrence of unfavourable acoustic phenomena. The inspiration from bionics influences users’ perception of space, increases their feeling of comfort and makes the room more friendly. Inspiration from nature is therefore becoming an increasingly popular trend in the design of materials used to finish spaces intended for people. The aim of the study is to analyse the dynamic properties of raster plates - in particular their natural and forced vibration frequencies, as well as deformations under the influence of air flow from distributed air conditioning. As part of the work, the Ansys program was used to model a number of different slot geometries in simply supported square coffers slabs. Based on the created slab models, an analysis was made and general conclusions were drawn, so that in the near future it will be possible to design raster ceilings that suppress vibrations coming from air conditioning instead of propagating them additionally.

ABSTRACT. The French law relating to the energy transition, passed on August 2015, aimed to promote the proportion of green energy in the energy mix in France, with a proportion of land and marine wind energy production by 20% in 2028, corresponding to a production of electricity of 10 GW. Marine windturbine blades, in service, are subjected to combined mechanical stresses (torsion, bending, centrifugal force, impact) and environmental ageing (humidity, temperature). To minimize maintenance operations and optimize their service life, it is necessary to be able to estimate as accurately as possible the material and structure integrity. The majority of blades has a sandwich structure. Skins are in thermosetting resin/fiberglass laminates and core is made of polymer foam with localized reinforcements of resin/carbon fibers laminates. The understanding of the internal damage mechanisms is then an essential step of the knowledge of the structure integrity evolution. For this, sandwich samples are submitted to hygro-thermal ageing and low energy impact. These two kinds of ageing are representative of the life service of marine windturbine blades. Mechanical tests, at different ageing levels, show the influence of intern damages on the macroscopic behaviour of sandwich materials. In-situ, by acoustic emission monitoring, et post-mortem observations allow to have a better understanding of the kinetics of the damage mechanisms identified at different scales especially, the phenomena identified at the level of interval interfaces (skins/core and fibers/matrix).

ABSTRACT. The level of residual stresses in a part is an important data to consider when sizing it. Residual stresses can have detrimental effects on the properties and durability of parts. These are stresses trapped in the material without any external load being applied. They build-up during the manufacture and/or life of the piece. In this work, residual stresses are determined in different fiber-reinforced composite laminates. This type of material is particularly subject to residual stresses due to the mismatch in coefficient of thermal expansion between fibers and matrix. The incremental hole drilling is one of the most widely used methods for determining residual stresses. It consists of drilling a hole increment by increment through the thickness of the material and measuring for each increment the strains induced by the local redistribution of the residual stresses. These strains are then converted into stresses using coefficients called calibration coefficients, which are calculated by finite element simulations. The objective of this study is to better understand the influence of manufacturing conditions and the structure of the composites (reinforcement type and stacking) on the residual stress state in the materials. For this, the residual stresses are calculated by the incremental hole method in samples with different cure cycles, different stackings and different reinforcements. The experimental and numerical aspects of the method as well as the coupling of the two are presented.

ABSTRACT. This work’s long-term objective is to assess the continuity of material deformation at the grain- and mesoscopic scale from processing to subsequent mechanical loading using crystal plasticity strain gradient models. To that end, advanced digital image correlation (HR-DIC) is performed on a pre-deformed microstructure of an Inconel 718, in order to provide plastic localization and discrete slip events necessary to instantiate simulation volumes. A numerical non-local crystal plasticity model has been developed, and implemented using FFT spectral method, to take into account initial deformation gradients and to describe their evolution under different loading conditions. Advanced experiment/simulation dialogue is expected to predict both localization of plastic strain at the sub-grain level and the macroscopic stress-strain behavior in recrystallized and pre-deformed microstructures. The process history of this latter microstructure will be purposely generated using stress-path change strategies on bi-axial specimens.

ABSTRACT. A nanowire is an extremely thin wire-like 1D structure, with a diameter on the nanometer scale, typically ranging from a few to hundreds of nanometres, and high aspect ratio (length-to-diameter ratio). A nanowire network refers to a three-dimensional interconnected mesh or network of nanowires, typically with a complex porous microstructure. Recently, we demonstrated lab-scale synthesis of networks by gas-phase reaction of Floating Catalyst CVD, where grown 1D nanowires of SiC, Si, or carbon nanotubes form a macroscopic material with an interesting combination of mechanical, thermal, and electrical properties. Models for predicting the elastic properties and ductile fracture of nanostructured network materials are essential for understanding their mechanical properties at the nanoscale. A combination of experimental characterization and computational modeling can be used to accurately describe and predict their properties. Specifically, damage propagation in nanonetworks is a complex phenomenon, involving multiple types of damage, such as point defects, localized bundle separation, nanowires or bundles sliding and shear, resulting in ductile behaviour and superior toughness. Experimental microscopy and spectroscopy techniques can be used to detect changes in the network structure in situ as a crack grows and propagates. The goal of this work is to combine experimental methods with analytical models to describe the tensile mechanical properties, stress transfer and inherent structural toughness of the nanoscale network systems that results in their high damage tolerance. We use WAXS/SAXS methods to determine nanowire alignment and track its evolution during network stretching, in order to identify and separate the contributions of nanowire orientation and chemical composition to the global mechanical properties. The micromechanical models emerging from this work will be also applied to study damage-tolerance of nanowire network electrodes used for energy-storage devices and batteries.

ABSTRACT. Additive manufacturing processes are taking hold in the medical sector, enabling the production of patient-specific devices that improve patient care while reducing associated costs. In the case of Endovascular Aneurysm Repair (EVAR) procedures, 3D printing is used to provide patient-specific 3D models of anatomies, enhancing surgical training, enabling rehearsal of complex cases, and improving intra-operative procedures. Thanks to the PolyJet additive manufacturing process, these physical models can be printed by combining different soft and rigid photopolymer materials to reproduce the haptic feedback of the human aorta. While 3D printing has proven valuable in reproducing anatomical structures, accurately simulating stress and strain states in these printed models remains a significant challenge. This challenge stems from the need to understand the mechanical behavior of printed materials, especially in the PolyJet technology, which exhibits complex structure-process-properties relationships [1][2][3]. Existing studies primarily focus on the response of materials to uniaxial loading, not considering the materials' response to multiaxial loading experienced by the 3D-printed anatomical models during surgical procedures. This study enriches our understanding of the mechanical response via biaxial loading tests while considering the anisotropy of the printed materials. Due to the complex characterization of these multiaxial tests, the material properties are identified using an integrated digital image correlation method [4].

ABSTRACT. When designing a crystal plasticity model, a choice must be made between using either a full-field approach that offers a detailed solution in a small region of the material or a more statistically-sound solution found using a homogenisation (mean-field) method. Unfortunately, when using a mean-field approach, important information about the microstructure, such as the topology of its different elements and the relationships between them, is missed. Therefore, when different materials are differentiated only by their topology, mean-field models cannot capture these differences, and full-field simulations with large representative volume elements have to be used.

In this work, a new crystal plasticity framework, completely written in APL, is presented. APL is both an alternative to mathematical notation and a full-featured programming language. The language is particularly well suited for the solution of complex computational problems by domain experts.

The presented model allows the usage of different homogenisation schemes. In addition to classical options, such as the full-constrained and relaxed-constraints approaches of Taylor and Sachs, new homogenisation schemes that take into account the topology of the microstructure are introduced. This information is added into the model by considering a different environment for each crystallographic orientation based on the misorientation distribution, or even on different distributions for each direction.

The model is, first introduced, and then used for the solution of several example problems, using as input different syntectic microstructures.

ABSTRACT. In the near vacuum of space, metal-to-metal fusion in mechanisms that have undergone wear has been attributed to a number of mission failures. This phenomenon is otherwise known as cold-welding and occurs when the base metals are exposed after the oxidation or lubrication layer has been removed. This research is concerned with the potential application of cold welding as a repair method for spacecraft hull post-debris/micrometeoroid impact. Specifically, this paper details a cold-welding onset measuring technique using electrical contact resistance of cold welding CuSn6 rods and is verified first in atmospheric conditions. Factors that allow for cold welding at reduced forces will also be investigated. Since the 1930s, research has been carried out into cold welding adhesion mitigation using advanced coating and lubricant development. This research also shows cold welding occurring at low forces when in the near vacuum. It is possible however, to cold weld certain metals in terrestrial environment by the yielding metals into one another. Other factors that may reduce these forces include material ductility, surface cleanliness and roughness. Metal fusion (and the forces required for this) is difficult to detect in real-time, however, the Kelvin Double Bridge can be used to detect this by monitoring the electrical resistance and identifying markers. A milliohm meter (1-100mΩ) is currently under development for measuring the onset of cold welding in 3mm CuSn6 rods as a function of applied force using a custom test rig. The electronic circuit incorporates a MAX680 voltage monitor and an LT3092 precision current reference that allows resistance measurements through the application of Ohm's Law. The test rig is under development for the application of forces between 10–500N. Successful detection of cold-welding joints allows for further studies into surface preparation methods to minimize the applied forces for the fusion mechanism.

ABSTRACT. Thermoforming is a manufacturing process where heated viscoelastic materials, such as polymers, are moulded into specific shapes by applying heat, draping the softened material over a mould, and then allowing it to cool and solidify. During thermoforming, springback may occur as the material partially revert to their original shape when cooled after being stretched and moulded. This phenomena could lead to discrepancies in the geometry of the final shape with respect to the desired shape. Therefore, it is necessary to consider springback effects when designing the mould to be used in the process. In this project, a surrogate model is built in order to predict the springback during the thermoforming of foam core material panels. The surrogate model works by mapping the mould geometry (determined by a number of design parameters) with the surface of the material after thermoforming (determined by characteristic parameters of the final geometry). The training and testing data is built by performing Finite Element Simulations with ABAQUS software, sampling the space of possible surfaces, while Gaussian Processes (Kriging) models are used to build the surrogate, which is later used to navigate the design space and determine the optimal mould geometry.

ABSTRACT. AA2219, an aluminum-copper alloy, is extensively utilized in aerospace industries due to its exceptional weldability. Its robust strength, particularly at cryogenic temperatures, renders it a prime choice for applications such as cryogenic fuel tanks. The manufacturing of these fuel tanks predominantly involves welding processes, with TIG welding being a prevalent method.

This study characterizes AA2219 through uniaxial tensile tests conducted along and transverse to the weld direction. A specially designed cruciform sample ensures that the gauge area encompasses critical weld zones. Planar biaxial tensile tests are subsequently performed on these cruciform samples to elucidate the material behavior under welded conditions. The tests, executed in load control mode, encompass seven distinct load ratios (1:0, 2:1, 4:3, 1:1, 3:4, 1:2, and 0:1). The evolution of the yield locus is plotted and compared with that of the base material, revealing a substantial reduction in the material's safe zone post-welding. This reduction poses challenges for performing any forming operation. Fractography is employed to comprehend fracture behavior under various loading conditions. Additionally, Electron Backscatter Diffraction (EBSD) analysis is utilized to study microstructure evolution during the tests. The findings shed light on the mechanical response of AA2219 after welding, emphasizing the critical need to understand material properties for ensuring the structural integrity of components, particularly in applications demanding high strength at cryogenic temperatures.

ABSTRACT. Polypropylene (PP) thermoplastics stand out because of their biocompatibility, high operating temperature, low macromolecular adsorption, and nontoxicity. In biology and medicine, PP plastic is used to create reaction tubes for various research. Additionally, plastic is used in medicine to produce human implants. When microfluidic chips are developed, PP plastic allows high structural strength, stiffness, and low adsorption. In addition, PP plastic can be used as a thermal micro actuator in MEMS devices. Because PP plastic is thermoplastic, it is usually formed by the hot embossing method. As a result of the wide use of PP thermoplastics, the hot embossing production method has been improved by using ultrasonic vibration. The improvement allows plastics to be imprinted at lower temperatures and have lower residual stresses, leading to savings in production costs and higher quality parts. To select suitable ultrasonic hot embossing formation parameters, it is necessary to perform a DMA study and determine the G' storage and G' loss modules. In this study, the test was performed with a stretching machine that has a vibration option. Strain, stress, and phase lag were recorded during the experiment. DMA material analysis allows for the analysis of viscoelastic materials such as PP properties and the use of these data with a finite element model. Irrespective of the forming temperature, the DMA measurements showed that the storage modulus increased with increasing forming frequency. The loss module increased with low frequency. As the frequency increased, the loss module decreased.

ABSTRACT. The collagen fibers which provide mechanical reinforcement to the arterial wall cannot sustain compressive loads. The existing Generalized Structure-Tensor (GST) based formulations emulate this through a tension-compression switch criterion based on the fiber stretch. This approach, however, has the following drawbacks: 1. discontinuous stresses at the switch point, 2. inconsistent predictions of the fiber stretch due to the conditional constitutive relations, i.e., the fibers predicted to be in compression according to the anisotropic terms can be in tension after the switch is employed, and 3. identical responses in longitudinal and transverse shear of unidirectional fibers, contrary to experimental observations.

To address these concerns, we introduce a matched invariant based on the Seth-Hill strain measure that auto-annihilates the contribution from fibers in pure compression. This leads to a unitary & switchless constitutive relation. The matched invariant inherently contains the I5 invariant and, consequently, the different shear modes yield distinct responses. The definition of the matched invariant is generalized for distributed fibers using the GST approach.

A vanishing matched invariant-based GOH (Gasser-Ogden-Holzapfel [1]) constitutive relation with the same number of material parameters is obtained as a particular case corresponding to the Green-Lagrange strain. The constitutive relation with the general Seth-Hill strain resembles an anisotropic Ogden-like relation that can better control the relative magnitude of normal and shear stresses. For deformations devoid of shear, the proposed relations exclude the compressed fibers in a manner similar to that of the angular integration-based model proposed by Li et. al [2]. As evidenced by extensive fitting to planar biaxial and uniaxial data for various arterial tissues, the resulting unitary constitutive relations have significantly improved descriptive and predictive capabilities. The proposed switchless constitutive relation solves the discussed issues with little added complexity. This formulation is equivalent to using a modified and deformation-dependent structure tensor instead of the conventional GST, thereby eliminating the major hurdles associated with the use of a switch criterion.

References: [1]. Gasser, T. C., Ogden, R. W., & Holzapfel, G. A. (2006). Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of the royal society interface, 3(6), 15-35. [2]. Li, K., Ogden, R. W., & Holzapfel, G. A. (2018). Modeling fibrous biological tissues with a general invariant that excludes compressed fibers. Journal of the Mechanics and Physics of Solids, 110, 38-53.