Linear elasticity theory of pentagonal quasicrystals

We present general solutions of the inhomogeneous linear elastic equations for pentagonal quasicrystals. The equations are those obtained by minimizing the harmonic elastic energy which includes a nontrivial coupling between the phason and displacement variables. Our solutions are presented in terms of the Green’s functions for the elastic equations and allow the solution of any inhomogeneous linear elastic problem for pentagonal quasicrystals. They are also applicable to thin icosahedral plates, where the plane of the plate has pentagonal symmetry. We use our general solutions to find the displacement and phason fields surrounding a dislocation, and then derive the interaction energy of dislocations.