Generalized dynamics of moving dislocations in quasicrystals

TL;DR

This paper develops a comprehensive continuum theory for the dynamics of moving dislocations in quasicrystals, including dislocation density tensors, equations of motion, and force and energy balance laws, considering phonon and phason fields.

Contribution

It introduces a unified theoretical framework for dislocation dynamics in quasicrystals, incorporating both elastodynamics and elasto-hydrodynamics, and derives generalized force and energy balance laws.

Findings

Derived dislocation density and current tensors for quasicrystals.

Formulated equations of motion for dislocation dynamics.

Established generalized force and energy balance laws.

Abstract

A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bianchi identities. Next, we give the equations of motion for the incompatible elastodynamics as well as for the incompatible elasto-hydrodynamics of quasicrystals. We continue with the derivation of the balance law of pseudomomentum thereby obtaining the generalized forms of the Eshelby stress tensor, the pseudomomentum vector, the dynamical Peach-Koehler force density and the Cherepanov force density for quasicrystals. The form of the dynamical Peach-Koehler force for a straight dislocation is obtained as well. Moreover, we deduce the balance law of energy that gives rise to the generalized forms of the field intensity vector and the elastic power density of quasicrystals. The above balance laws are produced for both models. The differences between the two models and their consequences are revealed. The influences of the phason fields as well as of the dynamical terms are also discussed.