Inserted: 20 oct 2016
Last Updated: 29 jun 2017
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