FFT-based multiscale modeling of nonlinear microstructured materials

Modeling failure and progressive damage of composite materials presents a challenging task. Conventional macro mechanical methods and even closed form estimates are in many cases not sufficient to predict the appropriate mechanical material response. A more accurate way is to capture nonlinear material effects directly on the discretized material level in the framework of a numerical multiscale approach. In this contribution an efficient multiscale approach is proposed. The fine scale problem (material level) is rewritten in an integral equation of Lippmann-Schwinger type and solved efficiently using the fast-Fourier transformation (FFT). Advantages of this method are its efficiency in terms of memory consumption and computational time. Further the calculation is carried out on a regular voxel grid and could therefore directly be applied on 3D images like tomographies without using any complicated mesh generation. The macro problem can easily be integrated in a standard Finite Element framework which is used to solve the macroscopic BVP (component level).