Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework

TL;DR

This paper introduces an extended physically recurrent neural network (PRNN) that models rate-dependent, path-dependent heterogeneous materials under finite strain, significantly accelerating microscale simulations while preserving physics-based accuracy.

Contribution

The work develops a PRNN architecture capable of handling rate-dependent materials in a finite strain framework, integrating constitutive models to enhance accuracy and extrapolation.

Findings

Achieved three orders of magnitude speed-up over traditional micromodels.

Successfully modeled rate-dependent behavior and complex loading scenarios.

Demonstrated accurate predictions for unseen loading conditions.

Abstract

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.