Computational homogenization of defect driving forces

Due to the fact that many engineering materials and also biological tissues possess an underlying (heterogeneous) micro-structure it is not sufficient to simulate these materials by pre-assumed overall constitutive assumptions. Therefore, we apply a homogenization scheme, which determines the macroscopic material behavior based on analysis of the underlying micro-structure. In the work at hand focus is put on the extension of the classical computational homogenization scheme towards the homogenization of material forces. Therefore, volume forces have to incorporated which may emerge due to inhomogeneities in the material. With assistance of this material formulation and the equivalence of the J-integral and the material force at a crack tip, studies on the influence of the micro-structure onto the macroscopic crack-propagation are carried out.