A multiscale damage model for composite materials using a FFT-based method

Modeling failure and progressive damage of composite materials presents a challenging task and is currently subject of many research activities in the field of computational mechanics. Conventional methods which assume constant material coefficients or global failure criteria, are in many cases not sufficient to predict the appropriate mechanical material response. Composite failure occurs as a result of complex mesostructural damage mechanisms and therefore it is preferable to capture these nonlinear material effects directly on a finer scale. Hence, recent multiscale modeling and simulation techniques were developed to consider the mesoscopic material behavior. In this contribution we propose an alternative multiscale approach similar to FE 2. Nonlinear material effects caused by progressive damage behavior are captured on a finer length scale. The constituents are modeled explicitly and simple isotropic damage laws are used to describe the constitutive behavior. Henc e, the resulting material response is based on genuine physical effects and only a few material parameters are required which can be measured directly in physical experiments. The fine scale problem (material level) is reformulated into an integral equation of Lippmann-Schwinger type and solved efficiently using the fast Fourier transformation (FFT). The calculation is carried out on a regular voxel grid which can be obtained from 3D images like tomographies without using any complicated mesh generation. Furthermore, the fine scale problem is integrated in a standard Finite Element framework which is used to solve the macroscopic BVP (component level).