Riccardo Scala
CMAF-CIO
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 times the lattice spacing, it is energetically convenient to have 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.
This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.
