An implicit coupled method of scaled boundary finite element and peridynamics for fracture analysis

In this paper, firstly, an innovative multi-scale coupled method based on scaled boundary finite element (SBFEM) and peridynamics (PD) is proposed for predicting fracture propagation of elastic bodies in static/quasi-static problems. The coupled process in this method is established not by transition regions (overlapping regions), but by force equilibrium conditions at common points, which greatly reduces the complexity of modeling. The SBFEM is introduced to model the non-cracked domain and the PD is applied to model the cracked domain in this method. This reduces a great deal of computational time compared to the PD method. Moreover, the limitations of surface effects and troublesome load conditions for the PD calculation can be eliminated or mitigated. The SBFEM is different from FEM in that only the boundary of elastic bodies is discretized. Therefore, the computational efficiency is further improved compared with the coupled method of the FEM and PD. The SBFEM is also different from BEM in that it does not need to provide the fundamental solution and compute the singular integrals. Hence, the method is more convenient for solving complex problems compared with the coupled method of the BEM and PD. The accuracy of this coupled method is demonstrated by one example of accuracy analysis for single coupled and multiple coupled interfaces, and three examples of fracture propagation analysis (two pre-determined cracks and one spontaneous crack). The results show that the coupled method has a high accuracy. Furthermore, it is recommended that the spacing of the common points be set equal to the spacing of the PD material points so that the accuracy of the coupled method can be maximized. Finally, the cracking forms of a square plate with different shaped holes are explored. It shows that the proposed coupled method has potential for engineering applications.