Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials

Abstract

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.

An Eshelby inclusion in a nonlinearly coupled thermoelectric bi‐material and tri‐material

“…In a Cartesian coordinate system {𝑥 𝑖 } (𝑖 = 1, 2, 3), let H, T, 𝐉 and 𝐉 𝑢 be, respectively, the thermoelectric potential, temperature, electric current density vector and energy flux vector in a homogeneous and isotropic nonlinearly coupled thermoelectric material. The constitutive equations and equilibrium equations are [17][18][19][20]…”

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

“…For the two-dimensional problem of nonlinearly coupled transports of heat and electricity in a homogeneous and isotropic thermoelectric material, the thermoelectric field characterizing the thermoelectric potential, the electric current density, the temperature, and the energy flux can be expressed in terms of two analytic functions f (z) and g(z) of the complex variable z = x 1 + ix 2 as follows [5,[7][8][9] :…”

“…Thermoelectric materials have been found increasing applications in the fields of energy production, conversion, conservation, and nondestructive testing (NDT) due to their inherent property of coupled transports of heat and electricity [1][2][3] . In recent years, the effects of nonlinear thermoelectric coupling on the electro-thermo-mechanical responses of thermoelectric materials have been investigated by several authors [4][5][6][7][8][9][10][11][12][13] . However, certain important issues arising in the discussion of nonlinear thermoelectric materials remain unresolved.…”

Analysis of a hollow fiber in thermoelectric materials considering interfacial thermal resistance

“…It is found that the results of the temperature field presented in Figure 2 agree well with those obtained in refs. [21, 25]. Figure 2a shows that the maximum temperature difference in the matrix around the interface increases along with the increase of the thermal resistance.…”

“…As the von Mises fracture criterion is commonly used in semiconductors, we also analyze the effect of the external energy flux on the von Mises stress in the matrix around the interface. The von Mises stress is defined by [25] …”