Generalized dynamics of moving dislocations in quasicrystals

Abstract

A theoretical framework for dislocation dynamics in quasicrystals is provided according tothe continuum theory of dislocations. Firstly, we present the fundamental theory formoving dislocations in quasicrystals giving the dislocation density tensors and introducingthe dislocation current tensors for the phonon and phason fields, including the Bianchiidentities. Next, we give the equations of motion for the incompatible elastodynamics aswell as for the incompatible elasto-hydrodynamics of quasicrystals. We continue withthe derivation of the balance law of pseudomomentum thereby obtaining thegeneralized forms of the Eshelby stress tensor, the pseudomomentum vector, thedynamical Peach–Koehler force density and the Cherepanov force density forquasicrystals. The form of the dynamical Peach–Koehler force for a straight dislocationis obtained as well. Moreover, we deduce the balance law of energy that givesrise to the generalized forms of the field intensity vector and the elastic powerdensity 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 alsodiscussed.