Learning the Stress-Strain Fields in Digital Composites using Fourier Neural Operator

TL;DR

This paper introduces a Fourier neural operator framework that accurately predicts stress and strain fields in 2D composite microstructures, enabling high-fidelity, zero-shot generalization and super-resolution with minimal training data.

Contribution

The study demonstrates the effectiveness of Fourier neural operators in modeling complex composite microstructures, achieving high accuracy and generalization with limited data.

Findings

High-fidelity stress-strain predictions with few data

Zero-shot generalization to unseen geometries

Super-resolution of stress-strain fields from low-resolution inputs

Abstract

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely challenging due to the innumerable design combinations and prohibitive computational costs for physics-based solvers. In this study, we employ a neural operator-based framework, namely Fourier neural operator (FNO) to learn the mechanical response of 2D composites. We show that the FNO exhibits high-fidelity predictions of the complete stress and strain tensor fields for geometrically complex composite microstructures with very few training data and purely based on the microstructure. The model also exhibits zero-shot generalization on unseen arbitrary geometries with high accuracy. Furthermore, the model exhibits zero-shot super-resolution capabilities by predicting high-resolution stress and strain fields directly from low-resolution input configurations. Finally, the model also provides high-accuracy predictions of equivalent measures for stress-strain fields allowing realistic upscaling of the results.