Abstract：In this paper，the problem of a circular hole with periodic radial cracks in thermoelectric material subjected to the uniform electric current and energy flux is studied. Considering the electrical and thermal impermeable boundary conditions，the exact solutions of electric current density，energy density and stress field in thermoelectric material are obtained by using complex function theory and conformal mapping method. According to the theory of fracture mechanics， the electric current，energy and stress intensity factors of periodic cracks are obtained by using Cauchy integral formula. The numerical results show that the intensity factors are proportional to the applied far-field loads，and these field intensity factors are closely related to the radius of the circular hole and the length of the crack. The results of this paper can promote the establishment of fracture mechanics theory system of thermoelectric material， and provide technical support for the reliability design and optimization of thermoelectric components.
2022, Vol. 43 
