Viscoelasticity from a Microscopic Model of Dislocation Dynamics

TL;DR

This paper demonstrates that the microscopic dynamics of dislocations and defects in a 2D crystal can be effectively described by hydrodynamic equations of viscoelasticity, linking microscopic defect densities to macroscopic relaxation times.

Contribution

It derives a microscopic basis for viscoelastic behavior in crystals, connecting dislocation density to Maxwell model relaxation times and incorporating short-scale bond order effects.

Findings

Viscoelasticity in 2D crystals is governed by hydrodynamic equations.

Relaxation times are expressed in terms of microscopic defect densities.

Short-scale effects modify relaxation times via wavevector dependence.

Abstract

It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. 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, bond orientational order effects become important and lead to wavevector dependent corrections to the relaxation times.