Analysis of inhomogeneous materials at large strains using fast Fourier transform

Abstract

invited lecture at the IUTAM Symposium - Stuttgart 2001International audienceThis paper focuses on a numerical method which has been recently developed to analyze the response of highly inhomogeneous materials, often with complex microstructure. This numerical method is based on Fast Fourier Transforms and allows to make direct use of digital images of the ”real” microstructure in the numerical simulation. The case of elastic nonhomogeneous phases is reduced to an integral equation (Lippman- Schwinger equation) which is solved iteratively. A nice feature of the method is that it involves a multiplication in Fourier space, a multiplication in real space, a FFT and an inverse FFT. The two first operations can be easily parallelized. It has been extended to various nonlinear behaviours (elastoplasticity, phase transformations, 3d analysis of texture evolution in polycrystals). Our work has been mainly concentrated on providing reference results to assess the accuracy of theoretical estimates for nonlinear compos- ites with simple behaviours (ideally plastic or power-law materials)