Simulation of Crack Propagation in Heterogeneous Materials by a Fracture Phase Field

We examine a method to compute the unknown fracture toughness of a heterogeneous material by the means of a time dependent boundary condition. This boundary condition imposes a steadily propagating crack on an exactly defined heterogeneous body, from which it is possible to derive the corresponding fracture toughness of the underlying material. The goal is to identify toughening mechanisms and to compute the toughness parameter for the particular material definition, without restricting the model to randomness or small contrast.