The Mathematical Institute, University of Oxford, Eprints Archive

Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock

Ockendon, J. R. and Voskoboinikov, Roman and Chapman, S. J. (2007) Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock. Journal of the Mechanics and Physics of Solids, 55 (9). pp. 2007-2025. ISSN 0022-5096

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Abstract

A mathematical methodology for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations in a single slip pane under the action of an external force in the direction of a locked dislocation in that plane is considered. As $n \rightarrow \infty$ there is a well-known formula for the number density of the dislocations, but this density is singular at the lock and it cannot predict the stress field there or the force on the lock. This poses the interesting analytical and numerical problem of matching a local discrete model near the lock to the continuum model further away.

Item Type:Article
Uncontrolled Keywords:Dislocation; Laguerre polynominals; Asymptotic expansion; Discrete; Density
Subjects:O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:630
Deposited By:John R. Ockendon
Deposited On:25 Jul 2007
Last Modified:20 Jul 2009 14:23

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