Line Defects in Two-Dimensional Dodecagonal Quasicrystals

In this work, line defects in two-dimensional dodecagonal quasicrystals are investigated. Using the ten-dimensional framework of the integral formalism of two-dimensional quasicrystals, the closed-form solutions for the displacement fields and stress functions of line defects, which are dislocations and line forces, in two-dimensional dodecagonal quasicrystals of Laue class 18 are derived. In dodecagonal quasicrystals, the phonon and phason fields are decoupled. The three phonon displacement components, two phason displacement components, three phonon stress functions and two phason stress functions of a straight dislocation and a line force are computed for a two-dimensional dodecagonal quasicrystals of Laue class 18. The self-energies of a straight dislocation and a line force are given. Moreover, the two-dimensional Green tensor is derived for two-dimensional dodecagonal quasicrystals of Laue class 18 within the framework of the integral formalism.