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Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials
Author(s) -
Yu ChuanBin,
Yang HaiBing,
Li YuHao,
Song Kun,
Gao CunFa
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800240
Subject(s) - thermoelectric effect , materials science , electric field , nonlinear system , stress (linguistics) , heat flux , field (mathematics) , multiphysics , discontinuity (linguistics) , thermoelectric materials , thermal , composite material , mechanics , stress field , finite element method , thermal conductivity , heat transfer , physics , mathematical analysis , mathematics , thermodynamics , linguistics , philosophy , quantum mechanics , pure mathematics
Thermoelectricity is a class of material possessing the ability of interconverting heat and electricity. For the sake of high conversion efficiency, inclusions/fibers are usually introduced into thermoelectric materials. However, the discontinuity of material property and geometry brought by inclusions/fibers might result in severe stress concentration and thus greatly affect the mechanical properties of thermoelectric material in its engineering service. This paper introduces a nonlinear coupled thermal–electrical–mechanical formulation for the plane problem of a circular inhomogeneity embedded in a thermoelectric medium under a combined uniform electric current density and energy flux. A special attention is directed towards the induced thermal stress field which has often neglected in the literature. Using methods based on Cauchy integrals, the complex potentials of the electric field, temperature field and associated stress field are derived explicitly in both the inhomogeneity and the surrounding matrix. The analysis shows that the electrically and thermally induced stress has a linear relationship with the energy flux applied at infinity, but has a nonlinear relationship with the remote electric current density. Numerical simulations are also performed to examine how the inhomogeneity influences the electrically induced thermal stress concentration on the interface. The presented results can be directly used for reliability consideration in design and optimization of thermoelectric composites with circular fibers/inclusions.