# Analysis of cell size effects in atomistic crack propagation

## TL;DR

This paper investigates how cell size influences crack propagation in crystalline materials, revealing bifurcation behavior and providing mathematical proofs for finite-cell approximation convergence.

## Contribution

It introduces a bifurcation analysis framework for crack propagation, demonstrating the stress intensity factor as a key parameter and analyzing finite-cell approximation convergence.

## Key findings

- Stress intensity factor acts as a bifurcation parameter
- Bifurcation diagram exhibits a periodic snaking curve
- Finite-cell approximations converge to the exact bifurcation diagram

## Abstract

We consider crack propagation in a crystalline material in terms of bifurcation analysis. We provide evidence that the stress intensity factor is a natural bifurcation parameter, and that the resulting bifurcation diagram is a periodic "snaking curve". We then prove qualitative properties of the equilibria and convergence rates of finite-cell approximations to the "exact" bifurcation diagram.