On the use of scaled boundary shape functions in adaptive phase field modeling of brittle fracture

This paper addresses the numerical modeling of brittle fracture using a phase field approach. We propose solving the coupled phase field / displacement problem by employing the scaled boundary finite element method, which facilitates the use of hierarchical meshes. An adaptive meshing approach based on this method is summarized. Contrary to existing applications of the scaled boundary finite element method in the context of phase field modeling, scaled boundary shape functions are employed in both staggered and monolithic solution schemes. The proposed methodology is verified considering two-dimensional benchmark problems. Very good agreement with finite element results of the force-displacement curves and crack paths is observed regardless of the solution scheme or meshing strategy.