Mesh refinement procedures for the phase field approach to brittle fracture

Two refinement procedures for phase field approach are proposed and their numerical performances are investigated in the solution of fracture problems. Starting from a coarse discretization of the domain, an energetic criterion is used to determine the active zones where damage initiates, evolves and mesh refinement is mandatory to accurately approximate crack topology. Moreover, the extension of the refined regions is strictly correlated with the size of the process zone defined by the optimal profile. Global and global/local refinement strategies are investigated. In particular, the global/local technique solves the displacement and phase field problems on a local mesh dynamically updated and adaptively refined during the computation. Once the solutions of the local problems are obtained, the phase field is interpolated back onto the original mesh, adequately refined where a damage threshold is exceeded. The performances of the refinement techniques are analyzed and compared in representative examples with stable and brutal crack propagation.