  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.
