Peridynamic stress is a weighted static Virial stress

TL;DR

This paper reveals that the peridynamic stress tensor can be expressed as a weighted static Virial stress, simplifying its numerical computation.

Contribution

It establishes a mathematical equivalence between the peridynamic stress tensor and a weighted static Virial stress, enhancing computational efficiency.

Findings

Peridynamic stress tensor is equivalent to a weighted static Virial stress.

Provides a simpler formula for numerical implementation.

Facilitates more efficient peridynamic stress calculations.

Abstract

The peridynamic stress tensor proposed by Lehoucq and Silling (2008) is cumbersome to implement in numerical computations. In this note, we show that the peridynamic stress tensor has the mathematical expression of a weighted static Virial stress derived by Irving and Kirkwood (1950), which offers a simple and clear expression for numerical calculations of peridynamic stress tensor.