On the equations of motion of dislocations in quasicrystals

•Three models of the dynamics of quasicrystals are investigated.•Elastodynamic model of wave type, elasto-hydrodynamic model and elastodynamic model of wave-telegraph type.•Equations of motion for the elastic distortion tensors and the elastic velocity vectors.•Sources for the elastic fields: phonon and phason dislocation density and dislocation current tensors.•Equations of motion for the displacement fields in the theory of incompatible elastodynamics.

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.