Homogenization of Interaction Energy of Dislocation Loops

Abstract

We consider the sum of interaction energies of an array of dislocation loops placed on a homogenization lattice as the lattice spacing and diameter of the loops tend to zero. Under suitable well-separation and L2 -boundedness assumptions, a formula for the limit of the total interaction energy is derived in terms of the weak limit, the generated H-measure and the generated Wigner measure of the associated Burgers vectors and oriented surface areas.