A novel linear elastic constitutive model for continuum-kinematics-inspired peridynamics

Abstract

Javili et al. recently reported a continuum-kinematics-inspired peridynamic model, in which theoretical aspects regarding the balance of linear and angular momentum and other conservation principles are considered. However, the analytical formulation of the model constants and the microelastic potential energy functions and numerical implementation were not defined. In this paper, a novel linear elastic constitutive model is proposed for the continuum-kinematics-inspired peridynamics by introducing specific expressions for various interaction potentials. The one-neighbor interaction potential equivalent to conventional bond-based interaction potential is utilized to account for the constitutive relationship within line elements between two material points. In contrast, the two- and three-neighbor interaction potentials are employed to consider the areal and volumetric effects under general mechanical loads. Three relevant material parameters are introduced and derived from energy equivalence to a classical linear elastic continuum mechanics model. Equipped with the three types of interaction potentials, the novel continuum-kinematics-inspired peridynamics is extended from classical bond-based peridynamics, wherein the two interaction force vectors within a bond are unequal and not parallel to the bond direction, can be regarded as an alternative version of non-ordinary state-based peridynamics. The proposed model is numerically demonstrated to be effective in absolutely eliminating the restriction of the fixed Poisson’s ratio in classical bond-based peridynamics, notably improving the effectiveness of the other enriched bond-based peridynamics in reproducing the elastic deformation of solids subjected to heterogeneous deformation fields and completely removing the numerical oscillations in non-ordinary state-based peridynamics.