Calculus of Variations and Geometric Measure Theory
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I. Lucardesi - M. Morandotti - R. Scala - D. Zucco

Confinement of dislocations inside a crystal with a prescribed external strain

created by morandott on 20 Oct 2016
modified on 29 Jun 2017


Submitted Paper

Inserted: 20 oct 2016
Last Updated: 29 jun 2017

Year: 2016

ArXiv: 1610.06852 PDF

Preprint SISSA 20$/$2016$/$MATE


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 $\Gamma$-convergence theory, in the framework of the so-called core radius approach.

Keywords: dislocations, core radius approach, divergence-measure fields, harmonic functions


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