Viscoelasticity from a microscopic model of dislocation dynamics

It is shown that the dynamics of a viscoelastic medium can be modeled as that of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects. At the longest length scales the viscoelasticity is described by the simplest Maxwell model, whose shear and compressional relaxation times are obtained in terms of microscopic quantities, including the density of free dislocations. At short length scales, t bond orientational order effects become important and lead to wave vector dependent corrections to the relaxation times.