FFT-based homogenization algorithm using digital images

Abstract

The applicability of the FFT-based algorithm for evaluating the mechanical behaviors of composites is investigated from practical view points. After the iterative numerical algorithm is presented, the computational efficiency is compared with that for conventional FEM-based homogenization algorithm and then extended to nonlinear analyses such as elastoplastic problems. In addition to preferable features in microstructural analyses, there are several advantages over the conventional approach by the FEM-based homogenization method. While the method is for evaluating the micromechanical response to the macroscopic deformation, the solution method can also be utilized to estimate the homogenized material constants. In the numerical examples, the digital image processing technique is extensively utilized to define the geometry of microstructures so that the method would not suffer from modeling effort.