Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria

TL;DR

This paper compares two bond-failure criteria in peridynamics, revealing their fundamental differences and impacts on fracture behavior through analytical proofs and numerical simulations.

Contribution

It provides a rigorous mathematical comparison showing the non-equivalence of critical stretch and energy density criteria in bond-based peridynamics.

Findings

Critical stretch and energy density criteria lead to different fracture patterns.

Numerical simulations demonstrate distinct crack propagation behaviors.

Theoretical proof of non-equivalence in bond failure criteria.

Abstract

This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numerically two common bond-failure criteria:~{\em critical stretch} and~{\em critical energy density}. In the former, bonds fail when they stretch to a critical value, whereas in the latter, bonds fail when the bond energy density exceeds a threshold. By focusing the analysis on bond-based models, we prove mathematically that the critical stretch criterion and the critical energy density criterion are not equivalent in general and result in different bond-breaking and fracture phenomena. Numerical examples showcase the striking differences between the effect of the two criteria on crack dynamics, including the crack tip evolution, crack propagation, and crack branching.