Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework
<|reference_start|>Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework: In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding them in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained.<|reference_end|>
@article{maia2024physically,
    title={Physically recurrent neural network for rate and path-dependent
  heterogeneous materials in a finite strain framework},
    author={M. A. Maia, I. B. C. M. Rocha, D. Kovav{c}evi'c, F. P. van der Meer},
    journal={arXiv preprint arXiv:2404.17583},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17583},
    primaryClass={cond-mat.mtrl-sci cs.LG cs.NA math.NA}
}