Renormalized energy for dislocations in quasi crystals
Abstract Anti plane shear deformations of a hexagonal quasi crystal with multiple screw dislocations are considered. Using a variational formulation, the elastic equilibrium is characterized via limit of minimizers of a core regularized energy functional. A sharp estimate of the asymptotic energy when the core radius tends to zero is obtained using higher order G convergence. Also, the interaction between dislocations and the Peach Kohler force at each dislocation are analyzed.