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

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 DNS results, efficiently computed via a newly developed fast Fourier transform (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.