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Confinement of dislocations inside a crystal with a prescribed external strain

TitleConfinement of dislocations inside a crystal with a prescribed external strain
Publication TypeJournal Article
Year of Publication2016
AuthorsLucardesi, I, Morandotti, M, Scala, R, Zucco, D
Abstract

We study screw dislocations in an isotropic crystal undergoing antiplane shear.
In the framework of linear elasticity, by fixing a suitable boundary condition for the strain
(prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.

URLhttp://urania.sissa.it/xmlui/handle/1963/35247

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