A non-ordinary state decomposition method for three-body potential peridynamics model

Abstract

A non-ordinary state decomposition method is proposed for the bond shear form of three-body potential peridynamics (PD) model. To accomplish this formulation, the effective relative displacement between two points is first decomposed into the volumetric and deviatoric parts based on the definition of dilatation. Starting from this, we give decomposition forms of the elementary deformations and strain energy density of this PD model and finally express the PD force function in the form of the sum of dilatational and distortional parts, which enable the PD model to clearly reflect material response dependence on volume changes and shape distorsion. Combined with the computational scheme of strain and stress tensors presented in the paper, the proposed method is validated numerically. The study permits the possibility of introducing plastic incompressibility for the three-body potential PD model.