An ordinary state-based peridynamic elastoplastic 2D model consistent with J2 plasticity

Abstract

A new ordinary state-based peridynamic model (OSB-PD) in 2D consistent with J2 plasticity using a novel decomposition for force and extension states is presented. A novel strategy for testing the consistency of an OSB-PD formulation for elastoplasticity is introduced. In contrast with other similar models, the new elasto-plastic OSB-PD model is objective and works for large rotations. Two rate-independent yield functions equivalent to J2 plasticity with associated flow rules are formulated based on force states and on the strain energy density. An efficient return mapping algorithm for peridynamic formulations in plasticity is proposed. The model is verified against results obtained with Abaqus for the classical formulation using two examples, one featuring plastic deformations under large rotations. The evolution of the plastic zone computed with the new model is found to match that from the classical model computed with Abaqus. With a simple damage model, a demonstrative plane stress example for shear localization and full rupture captures the same failure mechanism as observed experimentally: an initial almost symmetrical shear banding, evolves into a single, predominant shear band, followed by full rupture.