Hudson, Thomas and Ortner, Christoph (2014) Existence and stability of a screw dislocation under anti-plane deformation. Archive for Rational Mechanics and Analysis, 213 (3). pp. 887-929. doi:10.1007/s00205-014-0746-9 ISSN 0003-9527.

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Abstract

We formulate a variational model for a geometrically necessary screw dislocation in an anti-plane lattice model at zero temperature. Invariance of the energy functional under lattice symmetries renders the problem non-coercive. Nevertheless, by establishing coercivity with respect to the elastic strain and a concentration compactness principle, we prove the existence of a global energy minimizer and thus demonstrate that dislocations are globally stable equilibria within our model.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Crystal lattices, Crystalline polymers -- Defects -- Mathematical models
Journal or Publication Title:	Archive for Rational Mechanics and Analysis
Publisher:	Springer
ISSN:	0003-9527
Official Date:	September 2014
Dates:	Date Event September 2014 Published April 2014 Available
Volume:	213
Number:	3
Page Range:	pp. 887-929
DOI:	10.1007/s00205-014-0746-9
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	27 December 2015
Date of first compliant Open Access:	27 December 2015
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/H003096 (EPSRC), EP/E035027/1 (EPSRC)

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