An improved plane strain/plane stress peridynamic formulation of the elastic-plastic constitutive law for von Mises materials

A two-dimensional ordinary state-based peridynamic formulation is proposed for the analysis of elastic-plastic plane structures. Selecting appropriate relation for isotropic extension state, the deviatoric strain energy formulation is derived for plane strain/plane stress cases. Simple formulas to calculate peridynamic equivalent von Mises stress and its equivalent plastic strain are proposed. New yield function and flow rule are introduced. Implicit backward Euler time integration is used to obtain the increment of deviatoric plastic extension. Two example problems of grooved plate specimen and perforated plate under uniform tensile loading are considered to verify the accuracy of the present model in plane strain and plane stress situations respectively. The obtained results had a good agreement with those obtained by finite-element method. Results of displacements, von Mises stress, equivalent plastic strain, and plastic zone area are demonstrated. The effect of influence function on the results is also studied.