Statics and dynamics of dislocations: A Gamma-convergence approach.

In Materials Science, dislocations are 1D defects in the periodic structure of crystals whose presence (and motion) is believed to be the main mechanism of plastic deformations in metals. we consider a 2D model in which dislocations are introduced as point topological defects of the strain field. We draw a parallel between them and the vortices in superconductors, studied within the Ginzburg-Landau framework, pointing out similarities and differences between these two kinds of singularities. Finally, we present some recent results relative to the statics and dynamics of screw dislocations using a purely variational approach based on Gamma-convergence and on the minimizing movements method. The results are obtained in collaboration with Roberto Alicandro, Adriana Garroni and Marcello Ponsiglione.