Complex potential theory for the plane elasticity problem of decagonal quasicrystals and its application

The complex potential theory of two-dimensional decagonal quasicrystals is constructed and the complex variable method of Muskhelishvili is developed. Based on the complex representation of stresses and displacements, the arbitrariness and restrictions on the complex potentials are discussed. As an illustration of the complex potential theory, a decagonal quasicrystals plate with an elliptic notch under the action of stretch is considered. Some special cases of the results are also observed, which are helpful to check the correctness of the complex potential theory.