A peridynamic plastic model based on von Mises criteria with isotropic, kinematic and mixed hardenings under cyclic loading

In this study, an elastoplastic model based on ordinary state-based peridynamic theory is presented. The von Mises yield criteria is used to describe plastic yielding and the equivalent plastic stretch is utilized as internal variable for the general form of isotropic hardening, the modified form of kinematic hardening and the mixed of isotropic and kinematic hardening. Like classical approach to plasticity, a plastic flow rule is proposed based on the yield function. The proposed plastic model is described in the thermodynamic framework and it is shown that the proposed plastic flow and hardening of the peridynamic model are satisfied the requirements of the second law of thermodynamics. The proposed plastic model is rate-independent and the quasi-static analysis is considered. A numerical approach is proposed for the elastoplastic model and Newton Raphson algorithm is used to solve the nonlinear peridynamic equations. The numerical validation of proposed peridynamic models are done by comparing the results of 2-D peridynamic models under cyclic loading with the results of finite element methods based on the classical local continuum mechanic assumptions. The numerical results show that the proposed PD elastoplastic model can predict plastic yielding and linear/nonlinear hardening of materials beyond initial yield stress accurately. Moreover, it is observed that the presented method it is capable of modeling the kinematic hardening and Bauschinger effect in cyclic loading too.