A Neural Network Transformer Model for Composite Microstructure Homogenization

Abstract

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 (ROMs) commonly enhance efficiencies but 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 of linearly elastic fibers in an elastoplastic matrix, the transformer network predicts the history-dependent, non-linear, and homogenized stress-strain response. Two methods for encoding microstructure features were tested: calculating two-point statistics using Principal Component Analysis (PCA) for dimensionality reduction and employing an autoencoder with a Convolutional Neural Network (CNN). Both methods accurately predict the homogenized material response. The developed transformer neural network offers an efficient means for microstructure-to-property translation, generalizable and extendable to a variety of microstructures. The paper describes the network architecture, training and testing data generation, and performance under cycling and random loadings.