Speaker
Description
The formulation and calibration of constitutive models is still a challenging task for materials which exhibit complex nonlinear elastic or inelastic behavior. For this reason, data-driven methods and in particular the use of neural networks (NNs) have become increasingly popular in recent years. NN-based approaches that fulfill essential physical conditions a priori, often referred to as physics-augmented neural networks (PANNs), have proven to be particularly suitable for this purpose [1].In this contribution, we present an approach based on PANNs [1,2,3] that are applied as macroscopic surrogate models for the expensive computational homogenization of representative volume elements (RVEs). Our approach allows the efficient finite element simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear elastic behavior on the macroscale within a data-driven decoupled multiscale scheme [4]. By using a set of problem-specific invariants as the input of the PANN and the Helmholtz free energy density as the output, essential physical principles, e.g., objectivity, material symmetry or thermodynamic consistency are fulfilled by construction [1]. The invariants are formed from structure tensors of 2nd, 4th or 6th order and the right Cauchy-Green deformation tensor. Besides the network parameters, the structure tensors are automatically calibrated during training so that the underlying anisotropy of the RVE is reproduced optimally. In addition, a trainable gate layer in combination with lp regularization is included to remove unneeded invariants automatically and improve interpretability. Within the proposed algorithm, a suitable set of structure tensors is automatically chosen [3]. The developed approach is exemplarily applied to several descriptive examples. Necessary data for the training of the PANN surrogate model are collected via computational homogenization of RVEs.
[1] Linden et al. (2023). Neural networks meet hyperelasticity: A guide to enforcing physics. Journal of the Mechanics and Physics of Solids, 179, 105363.
[2] Kalina et al. (2024). Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria. Computer Methods in Applied Mechanics and Engineering, 421, 116739.
[3] Kalina et al. (2024). Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions. arXiv preprint
arXiv:2410.03378.
[4] Kalina et al. (2023). FEANN: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining. Computational Mechanics, 71(5), 827-851.
