New RVE concept and FFT methods in micromechanics of composites subjected to body force with compact support

TL;DR

This paper introduces a novel RVE concept using body force fields with compact support and FFT methods, enabling efficient data generation and machine learning-based surrogate modeling for composite materials.

Contribution

It develops a new RVE approach with BFCS, combined with FFT-based simulations and ML models, to improve homogenization accuracy and computational efficiency in micromechanics.

Findings

Efficient dataset generation for localized field responses

Accurate ML surrogate models for macroscopic behavior

Reduction of boundary artifacts in RVE simulations

Abstract

We consider static linear elastic composite materials (CMs) with periodic structure. The core of the proposed methodology is the generation of a novel dataset using specially designed body force fields with compact support (BFCS), enabling a new RVE concept that reduces the infinite periodic medium to a finite domain without boundary artifacts. This functionally reduced RVE is used for translated averaging of direct numerical simulations (DNS) results, efficiently computed via a newly developed FFT-based solver for BFCS loading. The resulting dataset captures localized field responses and is used to train machine learning (ML) and neural networks (NN) models to learn effective nonlocal surrogate operators. These operators accurately predict macroscopic responses while reflecting microstructural features and nonlocal interactions. By accounting for field localization while simultaneously eliminating influences from finite sample size and boundary effects, it provides a physically grounded and data-driven framework for constructing accurate surrogate models for the homogenization of complex materials.