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

TL;DR

This work addresses the high computational cost of micromechanical simulations for rate- and path-dependent heterogeneous materials under large deformations. It introduces a Physically Recurrent Neural Network (PRNN) that embeds explicit constitutive models into a neural surrogate, enabling memory through internal variables and learning a mapping from macroscopic stretch to local stresses via fictitious material points; a polar-decomposed, finite-strain formulation ensures frame-indifferent predictions. The approach is demonstrated on a 3D RVE with transversely isotropic fibers and viscoplastic matrix, achieving three-orders-of-magnitude speed-ups while maintaining accuracy under extrapolated loading, rate changes, and unloading/reloading. The PRNN serves as a robust constitutive model within FE, reproducing relaxation, cyclic behavior, and off-axis rate-controlled responses with consistent tangents, offering substantial potential for fast multiscale analyses in composite materials and related systems.

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.

Figures (26)

• Figure 1: Micromodel and scheme of configurations used in the updated Lagrangian framework.
• Figure 2: Right polar decomposition on deformation gradient $\mathbf{F}$ resulting in the stretch and rotation tensors $\mathbf{U}$ and $\mathbf{R}$, respectively
• Figure 3: Use of PRNN in a general full-order solution setting with $\mathbf{F}^{\Omega}$ and $\widehat{\bm{\sigma}}^{\Omega}_{\textrm{F}}$ as input and output, respectively.
• Figure 4: New architecture of PRNN for finite strain framework.
• Figure 5: Encoder architecture applied to obtain the local strain of a fictitious material point $j$ based on the input $\mathbf{U}^{\Omega}$.