Filtering material properties to improve FFT-based methods for numerical homogenization

TL;DR

This paper introduces a filtering technique for material properties to enhance FFT-based numerical homogenization methods, reducing computation time and local field oscillations across various microstructures.

Contribution

It proposes a novel filtering approach that improves FFT-based homogenization, demonstrating its effectiveness in linear elasticity and potential in other physical contexts.

Findings

Filtering reduces local field oscillations.

Grid refinement decreases computation time.

The 2-layers filter is effective across different microstructures.

Abstract

FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green operators have been proposed to accelerate the method and/or improve the description of the local fields. In this short note, filtering material properties is proposed as a third complementary way to improve FFT-based methods. It is evidenced from numerical experiments that, the grid refinement and consequently the computation time and/or the spurious oscillations observed on local fields can be significantly reduced. In addition, while the Voigt and Reuss filters can improve or deteriorate the method depending on the microstructure, a stiff inclusion within a compliant matrix or the reverse, the proposed "2-layers" filter is efficient in both situations. The study is proposed in the context of linear elasticity but similar results are expected in a different physical context (thermal, electrical...).