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.
@article{arxiv.1905.13328,
title = {Analysis of cell size effects in atomistic crack propagation},
author = {Maciej Buze and Thomas Hudson and Christoph Ortner},
journal= {arXiv preprint arXiv:1905.13328},
year = {2020}
}