Physics informed neural networks for continuum micromechanics

TL;DR

This paper explores the use of physics informed neural networks for modeling nonlinear, heterogeneous microstructures in continuum micromechanics, addressing challenges in localized effects through domain decomposition and adaptive training.

Contribution

It introduces domain decomposition and adaptive training strategies to improve physics informed neural networks' ability to handle material inhomogeneities with sharp interfaces.

Findings

Domain decomposition accurately resolves nonlinear stress and displacement fields.

Adaptive training strategies enhance convergence in complex microstructures.

Method successfully applied to real-world microstructure data.

Abstract

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. In this work we consider material non-linearities invoked by material inhomogeneities with sharp phase interfaces. This constitutes a challenging problem for a method relying on a global ansatz. To overcome convergence issues, adaptive training strategies and domain decomposition are studied. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $\mu$CT-scans.