Quasistatic fracture evolution

TL;DR

This paper develops a nonlocal quasistatic fracture evolution model for interacting cracks, demonstrating energy decrease with each load step through theoretical proof and numerical examples.

Contribution

It introduces an implicit approach based on local stationarity and fixed point methods for modeling crack evolution, with proofs of energy decrease and practical numerical demonstrations.

Findings

Fracture evolution decreases elastic energy at each step.

Numerical examples confirm theoretical energy decrease.

Model handles complex crack interactions and geometries.

Abstract

Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture evolution decreases stored elastic energy with each load step as the cracks advance; provided the load increments are chosen sufficiently small. This is also seen in the numerical examples. The numerical examples include evolution of a straight crack, a crack propagating inside an L-shaped domain, and two offset inward propagating cracks.