General expressions for the elastic displacement fields induced by dislocations in quasicrystals

The set of partial differential equations satisfied by the phonon and phason displacement fields u and w in quasicrystals has been solved by means of Fourier transform and eigenstrain methods, and general expressions of the elastic displacement fields induced by dislocations in quasicrystals have been given in terms of the Green function. The elastic Green tensor functions for every kind of quasicrystal are discussed in detail. Finally, as an example, the displacement fields induced by a straight dislocation line along the periodic tenfold axis of decagonal quasicrystals (three-dimensional) are calculated.