A novel FFT-based phase field model for damage and cracking behavior of heterogeneous materials

A novel numerical method is developed for three-dimensional modeling of damage and cracking in heterogeneous rock-like materials. Two key issues are addressed. For the first issue, influences of materials heterogeneities such as pores and inclusions on damage evolution and cracking processes are investigated by a homogenization approach with Fast Fourier Transform technique. For the second issue, the nucleation and propagation of cracks from diffuse damage evolution are formulated in Fourier space and described by a phase-field method. To do this, an efficient numerical procedure is developed for the stress-strain relationships and crack phase field propagation. A new elastic degradation function is proposed in order to describe a large range of cracking processes. A range of heterogeneous materials with different microstructure are generated and performed numerically to study effects of pores and inclusions on the damage evolution and cracking process in heterogeneous materials.