Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.