Thermal mechanical coupling analysis of two-dimensional decagonal quasicrystals with elastic elliptical inclusion

In this paper, the thermal mechanical coupling problem of an infinite two-dimensional decagonal quasicrystal matrix containing elastic elliptic inclusion is studied under remote uniform loading and linear temperature variation. Combining with the theory of the sectional holomorphic function, conformal transformation, singularity analysis, Cauchy-type integral and Riemann boundary value problem, the analytic relations among the sectional functions are obtained, and the problem is transformed into a basic complex potential function equation. The closed form solutions of the temperature field and thermo-elastic field in the matrix and inclusion are obtained. The solutions demonstrate that the uniform temperature and remote uniform stresses will induce an internal uniform stress field. Numerical examples show the effects of the thermal conductivity coefficient ratio, the heat flow direction angle and the elastic modulus on the interface stresses. The results provide a valuable reference for the design and application of reinforced quasicrystal materials.