Renormalized Energy and Forces on Dislocations

Giovanni Leoni
Carnegie Mellon University
Department of Mathematical Sciences

We discuss, from a variational viewpoint, the equilibrium problem for a finite number of Volterra dislocations in a plane domain. For a given set of singularities at fixed locations, we characterize elastic equilibrium as the limit of the minimizers of a family of energy functionals, obtained by a finite-core regularization of the elastic-energy functional. We give a sharp asymptotic estimate of the minimum energy as the core radius tends to zero, which allows to eliminate this internal length scale from the problem.