A dynamic generalization of the Eshelby problem, the strain profile due to an inclusion or defect in an isotropic elastic medium, was considered. It was shown that the higher the oscillation frequency of the defect, the more localized was the strain field around the defect. It was then demonstrated that the qualitative nature of the interaction between 2 defects was strongly dependent upon their separation, frequency and direction; changing from a ferromagnetic- to an antiferromagnetic-like behavior. The method was generalized to a finite density of defects and it was shown that the interactions in assemblies of defects could be mapped to XY-spin-like models: with implications for frustration and frequency-driven pattern transitions.

Oscillating Elastic Defects - Competition and Frustration. J.Barré, A.R.Bishop, T.Lookman, A.Saxena: Physical Review B, 2006, 74[2], 024104 (6pp)