Volume 54, Number 6, November-December 2020
|Page(s)||1821 - 1847|
|Published online||31 July 2020|
Analysis of cell size effects in atomistic crack propagation
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK
2 School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
* Corresponding author: email@example.com
Accepted: 18 January 2020
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.
Mathematics Subject Classification: 65L20 / 70C20 / 74A45 / 74G20 / 74G40 / 74G60 / 74G65
Key words: Crystal lattices / defects / crack propagation / regularity / bifurcation theory / convergence rates
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.