An adaptive peridynamics material point method for dynamic fracture problem

An adaptive peridynamics material point method (APDMPM) is proposed for modeling dynamic fracture problems to fully take advantage of both the peridynamics (PD) and material point method (MPM). The PD is used to model the crack region of a continuum, while the MPM is used to model the remaining regions of the continuum. A hand-shake region is employed to transfer the interaction between the PD and MPM particles. The simulation region is initially discretized by MPM particles, which will be adaptively converted to PD particles based on their stress condition or connect relation to make the PD sub-region fit the damage area automatically. Several numerical examples, including spallation of Hopkinson bar , plate with a pre-existing crack and plate with a circular cutout under velocity boundary conditions, are studied to verify the proposed method. The numerical results show that the APDMPM can successfully predict the initiation and propagation of cracks without explicitly tracking crack surface, meanwhile improve the calculation efficiency and accuracy of the rest of the region.