Numerical simulation for quasi-static crack growth and dynamic crack branching by coupled state-based PD and XFEM

This paper presents a novel framework combining the state-based peridynamics (SBPD) with the extended finite element method (XFEM) for crack propagation in two-dimensional solids. Numerical examination is conducted fulfilling both the quasi-static and time-dependent loading conditions. The computational domain is partitioned into two regions: (a) SPBD region: the vicinity of crack tips and potential region where the crack is likely to propagate, and (b) XFEM region: the area behind the crack tip and the rest of the body. The salient features of the developed framework include: (a) avoiding requirement of a priori knowledge of enrichment functions like the conventional XFEM; (b) without fracture criteria for crack propagation; (c) no restriction on the value of Poisson’s ratio like the bond-based peridynamics; and (d) higher computational efficiency than the pure peridynamics. The efficiency and accuracy of the proposed framework are systematically demonstrated through benchmark examples involving quasi-static crack growth and dynamic crack branching problems.