Abstract In this paper, the two-dimensional problem of a circular hole with two unequal cracks in infinite thermoelectric materials subjected to a uniform electric current and thermal flux is studied. Meanwhile, the boundary conditions at hole and cracks are assumed to be electrically impermeable and thermally impermeable. By using the complex function method and the conformal mapping theory, the exact solutions of the electric current density and the total energy flux are obtained. Furthermore, according to the theory of fracture mechanics, the intensity factors of electric current density, total energy flux density and stress at the crack tip have been obtained, which are proportional to the applied far-field loads, respectively. On the other hand, these field intensity factors are closely related to the radius of the circular hole and the lengths of cracks. The analytical solution is in good agreement with the regularized simulation results given by COMSOL commercial finite element code. Further numerical experiments reveal the effects of circular hole radius and lengths of cracks on the dimensionless thermoelectric and stress field intensity factors.

中文翻译：

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热电材料中与孔相邻的两条不等的裂缝扰动的热电场

摘要 本文研究了在均匀电流和热通量作用下无限热电材料中具有两条不等裂纹圆孔的二维问题。同时，假设孔洞和裂纹处的边界条件是不透电和不透热的。利用复函数法和共形映射理论，得到了电流密度和总能量通量的精确解。此外，根据断裂力学理论，得到了电流密度、总能量通量密度和裂纹尖端应力的强度因子，分别与施加的远场载荷成正比。另一方面，这些场强因子与圆孔半径和裂纹长度密切相关。解析解与 COMSOL 商业有限元代码给出的正则化仿真结果非常吻合。进一步的数值实验揭示了圆孔半径和裂纹长度对无量纲热电和应力场强度因子的影响。