On the equations of motion of dislocations in quasicrystals

In this work we investigate the theory of dynamics of dislocations in quasicrystals. We consider three models: the elastodynamic model of wave type, the elasto-hydrodynamic model, and the elastodynamic model of wave-telegraph type. Similarities and differences between the three models are pointed out and discussed. Using the framework of linear incompatible elastodynamic theory, the equations of motion of dislocations are deduced for these three models. Especially, the equations of motion for the phonon and phason elastic distortion tensors and elastic velocity vectors are derived, where the source fields are given in terms of the phonon and phason dislocation density and dislocation current tensors in analogy to the classical theory of elastodynamics of dislocations. The equations of motion for the displacement fields are also obtained.