An incremental bond-based peridynamic method for elastoplastic problems

The fracture problem of elastoplastic materials is an insistent challenge. It is difficult to implement the fracture simulations of elastoplastic materials in peridynamics (PD), especially in the bond-based peridynamic (BB-PD) framework. The core issue is how to introduce non-linear constitutive relationships into BB-PD model. To address this issue, an incremental form of BB-PD model was originally proposed. In the proposed model, a rapid strain identification technique was established. Based on this technique, the constitutive relationship is related to the deformation and the incremental bond force equation is formulated in a unified form. In addition, a fracture criterion controlled by energy was derived to implement plastic fracture simulations. Several numerical examples, including five elastoplastic deformation analyses and three quasi-static and dynamic fractures, were implemented to verify the feasibility and efficiency of the proposed model. The results show that the proposed model can accurately analyze the deformation of elastoplastic problems, especially plastic deformation. The numerical examples also demonstrate the fracture prediction capability of the proposed model.