Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition

An adaptive phase field method is proposed for crack propagation in brittle materials under quasi-static loading. The adaptive refinement is based on the recovery type error indicator, which is combined with the quadtree decomposition. Such a decomposition leads to elements with hanging nodes. Thanks to the polygonal finite element method, the elements with hanging nodes are treated as polygonal elements and hence do not require any special treatment. The mean value coordinates are used to approximate the unknown field variables and a staggered solution scheme is adopted to compute the displacement and the evolution of the phase field variable. A few standard benchmark problems are solved to show the efficiency of the proposed framework. It is seen that the proposed framework yields comparable results at a fraction of the computational cost when compared to standard approaches reported in the literature.