Elastic field for a straight dislocation in a decagonal quasicrystal

A straight dislocation line in a decagonal quasicrystal is considered. For a decagonal quasicrystal of point groups 10, and 10/ m with a straight dislocation parallel to the periodic direction, the basic governing equations are solved by decoupling this problem into a plane elasticity problem and an antiplane elasticity problem. For the latter, the solution is known; for the former, it is reduced to a single equation, , being the harmonic operator, by introducing a displacement function F . A general solution is formulated. Using a general solution and the Fourier transform, the explicit expressions for the dislocation-induced elastic field in a decagonal quasicrystal are obtained and the energy per unit length on the dislocation is given.