| Issue |
ESAIM: M2AN
Volume 54, Number 6, November-December 2020
|
|
|---|---|---|
| Page(s) | 1821 - 1847 | |
| DOI | https://doi.org/10.1051/m2an/2020005 | |
| Published online | 31 July 2020 | |
Analysis of cell size effects in atomistic crack propagation
1
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: buzem@cardiff.ac.uk
Received:
11
July
2019
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
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