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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:

Date	Event
18 January 2020	Accepted

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

RIOXX Funder/Project Grant:

Project/Grant ID	RIOXX Funder Name	Funder ID
EP/HO23364/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266
ECF-2016-526	Leverhulme Trust	http://dx.doi.org/10.13039/501100000275
EP/R043612/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266