A Multigrid Coupling Approach of the Extended Isogeometric–meshfree Method and Peridynamics for Brittle Fracture

A multigrid coupling approach of the extended isogeometric–meshfree (XIMF) method and bond-based peridynamics (PD) is developed for static and dynamic fracture problems. The coupling approach exploits the advantages of the XIMF method and PD, including the computational efficiency of the XIMF method and the generality of the PD in dealing with fracture problems. To couple the two methods, a problem domain is divided into the peridynamic and isogeometric–meshfree subdomains. The former subdomain aims to model both the crack-tip and potential cracking zone and is discretized by fine peridynamic points, while the latter corresponds to the remaining zone and is discretized by coarse isogeometric–meshfree meshes. The two subdomains are connected with the interface meshes, at which the ghost peridynamic particles are embedded and the displacement constraints are enforced. In this way, fracture patterns can be captured without requiring the crack-tip enrichment functions which are complicated in three dimensions while obtaining the comparable efficiency of the XIMF method. Furthermore, an adaptive switching strategy is proposed to convert the isogeometric–meshfree meshes into peridynamic particles. Finally, several representative benchmark problems including the two-dimensional static crack propagation in a double cantilever beam and dynamic crack branching, and the three-dimensional mixed-mode fracture in a skew-notched structure are attempted to validate the proposed approach.