Ordinary state-based peridynamic formulation for cyclic elastoplastic responses

Peridynamic (PD) constitutive relationship for cyclic elastoplasticity, especially Bauschinger effects, is still lacking, which hinders the full play of its unique advantages in fatigue analysis on problems of low-cycle-fatigue and effects of crack-tip plasticity. This study proposes an ordinary state-based peridynamic formulation for metal cyclic elastoplastic responses, in which the von Mises yield function, plastic flow rule and hardening law are respectively established, and the model parameters are calibrated to classical plasticity theory for both 2-dimensional cases (plane stress & plane strain) and 3-dimensional cases. For the first time, particularly, this study proposes the internal variable of back bond stretch in peridynamics to describe kinematic hardening, which enables the common kinematic hardening laws such as Chaboche law to be realized within the framework of peridynamic theory, and the formulation of material parameter calibration is also presented. Compared with analytical solutions by several typical benchmark examples, the proposed model fully demonstrates its capability of describing cyclic elastoplastic responses and cyclic hardening/softening effects, with $\delta$-convergence and $m$-convergence both achieved. The proposed model founds the basis for analyzing fatigue problems in which cyclic plasticity plays an important role.