The plane problem of a non-circular rigid inhomogeneity embedded in an infinite thermoelectric matrix under a uniform remote electric current is investigated based on the complex variable method. The inclusion is assumed to be electrically insulated and thermally conductive. Techniques of Faber and Fourier series are used to solve the corresponding boundary value problems. The obtained results show that the shape, bluntness and heat conductivity of the inclusion have a significant effect on the interfacial thermal stress distribution induced by the external electric current. In addition, the Von Mises stress concentration around a non-circular inclusion could be lower than that around a circular inclusion by designing the shape and orientation of the inclusion properly.

中文翻译：

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二维非线性热电材料中非圆形刚性夹杂物周围的电流感应热应力

基于复变量法研究了均匀远程电流作用下无限热电矩阵中嵌入的非圆形刚性不均匀性平面问题。假定夹杂物是电绝缘和导热的。使用 Faber 和傅立叶级数的技术来解决相应的边值问题。所得结果表明，夹杂物的形状、钝度和热导率对外部电流引起的界面热应力分布有显着影响。此外，通过适当设计夹杂物的形状和取向，非圆形夹杂物周围的 Von Mises 应力集中可以低于圆形夹杂物周围的 Von Mises 应力集中。