A novel boundary tracing method without enrichment for modeling cracks and their propagation

•An xIGFD method was developed for crack analysis by combing the IGFD discretization technique and the proposed boundary tracking method.•xIGFD could obtain high-precision parameters of fracture mechanics without enrichment or re-meshing.•Three boundary representation techniques were proposed for dealing with the degrees of freedom on the cracks' boundaries.•xIGFD predicted smoother crack propagation paths than those predicted by XFEM.