Classic dynamic fracture recovered as the limit of a nonlocal peridynamic model: The single edge notch in tension

TL;DR

This paper demonstrates that a simple nonlocal peridynamic model of brittle fracture converges to classical dynamic fracture mechanics as the nonlocality parameter approaches zero, supported by analytical and numerical evidence.

Contribution

It shows that the nonlocal peridynamic model recovers classical fracture behavior and kinetic relations in the limit of vanishing nonlocality, bridging nonlocal and classical theories.

Findings

Convergence of nonlocal model to classical fracture mechanics.

Recovery of kinetic crack relations from the nonlocal model.

Numerical validation of the convergence.

Abstract

A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic relation for the crack is recovered directly from the nonlocal model in the limit of vanishing nonlocality. We carry out our analysis for a single crack in a plate subject to mode one loading. The convergence is corroborated by numerical experiments.