Defects in Static Elasticity of Quasicrystals

A review on mathematical elasticity of quasicrystals is given. In this review, the focus is on various defects of quasicrystals. Dislocation and crack are two classes of typical topological defects, while their existence has great influence on the mechanical behavior of quasicrystals. The analytic and numerical solutions of dislocations and crack in quasicrystals are the core of the static and dynamic elasticity theory, and this paper gives a comprehensive review on the solutions for dislocations and crack with different configurations in different various important quasicrystalline systems. We review some results in linear elasticity of quasicrystals, referring to different boundary value problems. We also add some new achievements