Renormalized energy and Peach-Köhler forces for screw dislocations with antiplane shear

We present a variational framework for studying screw dislocations subject to antiplane shear. Using a classical model developed by Cermelli and Gurtin [6], methods of Calculus of Variations are exploited to prove existence of solutions, and to derive a useful expression of the Peach-K¨ohler forces acting on a system of dislocation. This provides a setting for studying the dynamics of the dislocations, which is done in [4].