Ockendon, J. R. and Voskoboinikov, Roman and Chapman, S. J. (2007) Continuum and discrete models of dislocation pileups. I Pileup at a lock. Journal of the Mechanics and Physics of Solids, 55 (9). pp. 20072025. ISSN 00225096

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Abstract
A mathematical methodology for analysing pileups of large numbers of dislocations is described. As an example, the pileup 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 there is a wellknown 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:  29 May 2015 18:25 
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