  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.
