Modification in Silling's Peridynamic Formulation of Elasticity Theory for Discontinuities and Long-Range Forces

TL;DR

This paper proposes a modified peridynamic equation of motion with an added damping term to reduce artificial oscillations in displacement fields, enhancing the stability of elasticity simulations involving discontinuities and long-range forces.

Contribution

The authors introduce a damping force term into Silling's peridynamic formulation, improving its stability and accuracy for modeling elastic materials with discontinuities.

Findings

Reduced artificial oscillations in displacement fields

Enhanced stability of peridynamic simulations

Potential for more accurate modeling of discontinuities

Abstract

We suggest modified version of Silling's peridynamic equation of motion within the framework of Silling's peridynamics formulation (J. Mech. Phys. Solids {\bf 48}, pp.175-209, 2000) of elasticity theory. The modified equation contains an additional damping force term. This term can eliminate artificial oscillations in displacement field at large values of time as predicted by Silling's peridynamic equation.