Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response

TL;DR

This paper introduces equivariant graph neural networks that inherently respect material symmetries to effectively model the anisotropic mechanical response of microstructured composites, improving prediction accuracy.

Contribution

The work develops neural network architectures that incorporate equivariance and tensor basis operations for homogenizing anisotropic microstructural materials.

Findings

Significant performance improvements over existing models.

Effective modeling of elastic and plastic deformation.

Applicable to diverse microstructural textures and phases.

Abstract

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.