Ordinary state-based peridynamics for nonlinear hardening plastic materials' deformation and its fracture process

In this paper, a modelling for ordinary state-based peridynamics to simulate plastic deformation is presented. This modelling can simulate nonlinear-hardening plastic mode, what's more, the perfect plastic model and linear-hardening plastic model can also be simulated in a simple way too. The expression of equivalent plastic stress in the formulation of nonlocal ordinary state-based peridynamics is established. The yield function is constructed based on the Von Mises yield criteria. Then the way to calculate the equivalent plastic stress in every step is established. And all the formulations have been discussed both in 2D case and 3D case. The validity of this modelling is established by comparing the results of a plate under tension or pushing simulated by peridynamics and FEM in 2D case, and the plate under tension is the plastic material with power-hardening law, the plate under pushing is the plastic material with linear-hardening law.