Virtual clustering analysis for phase field model of quasi-static brittle fracture

In this paper, we develop a Virtual Clustering Analysis method for a phase field model of brittle fracture. In addition to the strain/stress field, we treat the phase field variable via clusters as well, based on Green’s function of the governing Helmholtz equation. Around the crack path, we assign one cluster per cell. We detect the crack tip and recluster accordingly as the crack propagates. Three examples are presented to demonstrate the numerical efficiency of the proposed method, including either straight or curved crack, under tension or shear.