A theoretical framework for dislocation dynamics in quasicrystals was provided according to the continuum theory of dislocations. Firstly, the fundamental theory for moving dislocations in quasicrystals was presented; giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bianchi identities. Secondly, the equations of motion were given for the incompatible elastodynamics as well as for the incompatible elasto-hydrodynamics of quasicrystals. Thirdly, the balance law of pseudomomentum was derived, 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 was also obtained. Moreover, the balance law of energy that gave rise to the generalized forms of the field intensity vector and the elastic power density of quasicrystals was deduced. The above balance laws were produced for both models. The differences between the two models and their consequences were revealed. The influences of the phason fields as well as of the dynamical terms were also considered.

Generalized Dynamics of Moving Dislocations in Quasicrystals. E.Agiasofitou, M.Lazar, H.Kirchner: Journal of Physics - Condensed Matter, 2010, 22[49], 495401