A new peridynamic formulation with shear deformation for elastic solid

TL;DR

This paper introduces a novel peridynamic formulation incorporating shear deformation for elastic solids, improving damage modeling and crack propagation simulation in 2D and 3D.

Contribution

It presents a new peridynamic model with shear deformation and a damage rule based on maximal deviatoric bond strain, enhancing fracture simulation accuracy.

Findings

Accurate simulation of Mode I, II, and III crack propagation.

Effective modeling of shear deformation in elastic solids.

Validation through 2D and 3D numerical examples.

Abstract

We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.