Phase field method for quasi‐static brittle fracture: an adaptive algorithm based on the dual variable

Abstract

An adaptive phase field method for quasi‐static brittle fracture is developed. The adaptive refinement of the meshes is based on the error between two stresses: the discontinuous post‐processed stresses computed with the displacement approximation and a H(div) conforming dual approximation of the stresses. The algorithm is validated by solving a benchmark problem considering a plate with an edge crack subjected to tension load.