Learning the stress-strain fields in digital composites using Fourier neural operator

Area of Science:

• Materials Science
• Computational Mechanics
• Artificial Intelligence

Background:

• Advanced composite materials are crucial for high-performance applications.
• Designing tailored microstructures with desired properties is computationally intensive.
• Existing physics-based solvers face limitations due to complex geometries and vast design spaces.

Purpose of the Study:

• To develop an efficient computational framework for predicting the mechanical response of 2D composite materials.
• To leverage neural operators for accurate and fast material microstructure analysis.
• To overcome the challenges posed by complex hierarchical designs and high computational costs.

Main Methods:

• Implementation of a Fourier Neural Operator (FNO) framework.
• Training the FNO on microstructural data to learn mechanical responses.
• Evaluating the FNO's predictive accuracy on stress and strain tensor fields.
• Assessing zero-shot generalization capabilities on unseen geometries.
• Investigating zero-shot super-resolution for stress and strain fields.

Main Results:

• The FNO accurately predicts complete stress and strain tensor fields for complex 2D composite microstructures.
• High-fidelity predictions are achieved with minimal training data, solely based on microstructure.
• The model demonstrates excellent zero-shot generalization to arbitrary, unseen geometries.
• The FNO achieves zero-shot super-resolution, predicting high-resolution fields from low-resolution inputs.
• Accurate prediction of equivalent stress-strain measures enables realistic upscaling.

Conclusions:

• The Fourier Neural Operator provides a powerful and efficient tool for analyzing the mechanical behavior of advanced composite materials.
• This data-driven approach significantly reduces computational costs compared to traditional solvers.
• The FNO's capabilities in generalization and super-resolution open new avenues for accelerated materials design and discovery.