Electric and heat conduction across an elliptic cavity in an anisotropic medium

Abstract

It is well known that the anisotropy of materials will significantly affect heat conduction, and the corresponding results have been applied to the thermal analysis of materials. An elliptic cavity in a nonlinearly coupled anisotropic medium, on the other hand, is much more difficult to analyze. Based on the complex variable method, the problem of a two-dimensional elliptical cavity in an anisotropic material is analyzed in this paper, and the field distributions have been obtained in closed-form. The field intensity factors are discussed in detail. The results show that both the temperature and electric potential gradients at a crack tip are always perpendicular to the crack surface, regardless of the anisotropy and the nonlinearity in the constitutive equations and the arbitrariness of loading direction. These results provide a powerful tool to analyze the effective behavior and reliability of anisotropic materials with cavities.