Towards crack paths simulations in media with a random fracture energy

Simple probabilistic models of fracture of 3D polycrystals involving transgranular and intergranular cracks are proposed, based on undamaged paths and appropriate percolation thresholds. In a second part, we propose theoretical extensions of phase field models for crack initiation and propagation to the case of locally heterogeneous and anisotropic fracture energy, and their implementation to get full field solutions by means of iterations of Fourier transforms to replace the standard finite element approach. (C) 2019 Elsevier Ltd. All rights reserved.