A Neural Network Transformer Model for Composite Microstructure Homogenization

Heterogeneity and uncertainty in a composite microstructure lead to either computational bottlenecks if modeled rigorously, or to solution inaccuracies in the stress field and failure predictions if approximated. Although methods suitable for analyzing arbitrary and non-linear microstructures exist, their computational cost makes them impractical to use in large-scale structural analysis. Surrogate models or Reduced Order Models (ROM), commonly enhance efficiencies, but they are typically calibrated with a single microstructure. Homogenization methods, such as the Mori-Tanaka method, offer rapid homogenization for a wide range of constituent properties. However, simplifying assumptions, like stress and strain averaging in phases, render the consideration of both deterministic and stochastic variations in microstructure infeasible. This paper illustrates a transformer neural network architecture that captures the knowledge of various microstructures and constituents, enabling it to function as a computationally efficient homogenization surrogate model. Given an image or an abstraction of an arbitrary composite microstructure, the transformer network predicts the homogenized stress-strain response. Two methods were tested that encode features of the microstructure. The first method calculates two-point statistics of the microstructure and uses Principal Component Analysis for dimensionality reduction. The second method uses an autoencoder with a Convolutional Neural Network. Both microstructure encoding methods accurately predict the homogenized material response. The paper describes the network architecture, training and testing data generation and the performance of the transformer network under cycling and random loadings.