Material modeling in the era of AI: from sparse regression to the language of material laws

The lecture provides an overview of recent research conducted by the speaker's group and collaborators on the automated discovery of material models. This research advocates for a paradigm shift, moving away from the traditional approach of calibrating unknown parameters within a preselected material model towards a new objective of model discovery. This entails the simultaneous selection, generation, or encoding of the most suitable model to interpret given experimental data, along with the calibration of its unknown parameters. To achieve this goal, a variety of tools are employed, ranging from sparse regression to Bayesian learning, and from formal grammars to symbolic regression. Each of these tools possesses distinct features but shares the common aim of ensuring the fulfilment of physics constraints and interpretability of the discovered model(s). Initially developed to discover a specific model within a predetermined category (i.e. hyperelasticity, viscoelasticity or plasticity), the approach was more recently extended to to the general case of a material belonging to an unknown class of constitutive behavior. Additional relevant aspects such as the type of data, specimen design, and experimental validation are also discussed.  

Architected materials with tuned instabilities break the wall of hyperelasticity

Keywords: Flutter instability; Non-Hermitian mechanics; Homogenization

A way to implement controlled instabilities in architected materials is shown. In particular, elastic grids of axially prestressed rods are considered, to be deformed incrementally and thus involving incremental bending moment, and axial and shear forces. It is shown that tunable material instabilities can be designed, as well as the achievement of dynamical properties of wave localization and filtering. The emergence of material instabilities such as shear band formation is demonstrated both for compressive [1] and tensile axial forces [2]. Moreover, the architecture of the analyzed structures leads to the emergence of multiple band gaps, flat bands, and Dirac cones [3]. The experience gained on structural flutter [4, 5] is exploited to implement a new concept, namely, the possibility of implementing a Hopf bifurcation in a continuous medium. This possibility is proven through a rigorous application of Floquet-Bloch wave asymptotics, which yields an unsymmetric acoustic tensor governing the incremental dynamics of the effective material [6]. The latter represents the incremental response of a hypo-elastic solid, which does not follow from a strain potential and thus apparently breaks the wall of hyperelasticity, leading to non-Hermitian mechanics. The discovery of elastic materials capable of collecting or releasing energy in closed strain cycles through interactions with the environment introduces new micro and nano technologies and finds definite applications, for example, in the field of energy harvesting.

Acknowledgements Financial support from ERC-ADG-2021-101052956-BEYOND is gratefully acknowledged. 

References

[1]    Bordiga, G., Cabras, L., Piccolroaz, A., and Bigoni, D. “Dynamics of prestressed lattices: Homogenization, instabilities, and strain localization” J. Mech. Phys. Solids, 146, 104198 (2021).

[2]    Bordiga G., Bigoni D. and A. Piccolroaz “Tensile material instabilities in elastic beam lattices lead to a closed stability domain”. Phil. Trans. Royal Soc. A, Vol. 380, 20210388, (2022).

[3]    Cabras, L., Bigoni, D., and Piccolroaz, A. Dynamics of elastic lattices with sliding constraints. Proc. Royal Soc. A 480, 20230579, 2024.

[4]    Rossi, M., Piccolroaz, A., Bigoni, D., “Fusion of two stable elastic structures resulting in an unstable system” J. Mech. Phys. Solids, 173, 105201 (2023).

[5]    Bigoni, D., Dal Corso, F., Kirillov, O., Misseroni, D., Noselli, G., Piccolroaz, A. Flutter instability in solids and structures, with a view on biomechanics and metamaterials. Proc. Royal Soc. A 479, 20230523 (2023).

[6]    Bordiga, G., Piccolroaz, A., and Bigoni, D., “A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability” J