A numerical method for computing the overall response of nonlinear composites with complex microstructure

TL;DR

This paper introduces a Fourier series-based numerical method for computing the response of nonlinear composites with complex microstructures, avoiding meshing and directly utilizing microstructure images.

Contribution

It presents a novel Fourier series approach that bypasses meshing and extends to nonlinear constituents, enhancing computational efficiency and flexibility.

Findings

Accurately computes responses of complex microstructures

Extends to nonlinear materials through time-stepping

Flexible for various microstructure geometries

Abstract

The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.