Strength-based regularization length in phase field fracture

We propose a length-free (LF) implementation of phase field (PF) approach to fracture. The input parameters of the LF-PF model are the same as those of the coupled criterion (CC), namely the critical energy release rate G(c) and the material tensile strength sigma(c). This formulation relies on the previously determined correlation between the internal length in classical PF fracture models and the material tensile strength. Similar failure loads are obtained using either AT1 and AT2 versions of the LF-PF, a larger diffused damaged zone being observed using AT1. The LF-PF formulation allows retrieving the size effect for a crack under remote tensile stress in infinite medium and shows square hole specimen failure stresses close to the predictions obtained using the CC, which allows using both models in a complementary manner. Finally, the proposed formulation overcomes the problem of identifying different internal lengths for different specimen configurations.