A coupling approach of state-based peridynamics with node-based smoothed finite element method

In this work, a novel approach to couple ordinary state-based peridynamics (OSPD) with node-based smoothed finite element method (NS-FEM) is proposed. In present method, the solution domain is partitioned into two regions, one is discretized by OSPD, the other by NS-FEM, and more importantly, no transition region is introduced. The physical information is transmitted mutually from local to non-local regions, which is governed by the unified coupling equations of motion. The coupling takes full advantage of the generality of OSPD and the efficiency of NS-FEM. The parts of regions where damage and fracture either exist or are expected to propagate are described by OSPD, and the rest of regions are described by NS-FEM to reduce the computational cost and surface effect. Additionally, the critical bond work in OSPD is assumed to depend on the bond length, which is derived by the relation with the critical energy release rate in this study. Several numerical examples involving crack propagation are investigated under either dynamic or quasi-static conditions and satisfactory results have been obtained demonstrating the validity and efficiency of the proposed coupling approach.