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Analysis of cell size effects in atomistic crack propagation

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Buze, Maciej, Hudson, Thomas E. (Edward) and Ortner, Christoph (2020) Analysis of cell size effects in atomistic crack propagation. ESAIM: Mathematical Modelling and Numerical Analysis .

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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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Q Science > QD Chemistry
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Crystal lattices -- Mathematical models, Bifurcation theory
Journal or Publication Title: ESAIM: Mathematical Modelling and Numerical Analysis
Publisher: EDP Sciences
ISSN: 0764-583X
Official Date: 18 January 2020
Dates:
DateEvent
18 January 2020Accepted
Date of first compliant deposit: 23 March 2020
Status: Peer Reviewed
Publication Status: Forthcoming
Publisher Statement: “Reproduced with permission from EDP Sciences"
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: Copyright / Published by: EDP Sciences
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/HO23364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
ECF-2016-526Leverhulme Trusthttp://dx.doi.org/10.13039/501100000275
EP/R043612/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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