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Analysis of stable screw dislocation configurations in an antiplane lattice model
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Hudson, Thomas and Ortner, Christoph (2015) Analysis of stable screw dislocation configurations in an antiplane lattice model. SIAM Journal on Mathematical Analysis, 47 (1). pp. 291-320. doi:10.1137/140964436 ISSN 0036-1410.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1137/140964436
Abstract
We consider a variational antiplane lattice model and demonstrate that at zero temperature, there exist locally stable states containing screw dislocations, given conditions on the distance between the dislocations and on the distance between dislocations and the boundary of the crystal. In proving our results, we introduce approximate solutions which are taken from the theory of dislocations in linear elasticity and use the inverse function theorem to show that local minimizers lie near them. This gives credence to the commonly held intuition that linear elasticity is essentially correct up to a few spacings from the dislocation core.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0036-1410 | ||||||
Official Date: | 8 January 2015 | ||||||
Dates: |
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Volume: | 47 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 291-320 | ||||||
DOI: | 10.1137/140964436 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Open Access Version: |
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