Thermal stress concentration in thermoelectric material induced by a smooth inhomogeneity

Abstract

Thermal stress concentration in thermoelectric materials, induced by multiphysical field perturbations due to inherent inhomogeneities, is a primary driver of premature failure during service. A key bottleneck in modeling inhomogeneity system is the lack of an explicitly available solution. Motivated by this, the present work investigates the two-dimensional electro-thermo-elastic coupling problem of a smooth inhomogeneity characterized by a Laurent polynomial and embedded in a thermoelectric material subjected to uniform electric current density or uniform energy flux at infinity. The boundary conditions of electrical insulation, adiabatic behavior, and perfect mechanical bonding are considered. Within the framework of complex variable theory, once the explicit solutions for the electric and temperature fields are obtained, the elastic field can be solved via a newly developed iterative strategy. This approach decomposes the boundary value problem into a sequence of exactly solvable Riemann-Hilbert problems, which yields an explicit expression for the elastic field in terms of Faber polynomials and their associated polynomials. Numerical analyses for elliptical and polygonal inhomogeneities demonstrate that stress concentration predominantly occurs on the matrix side of the boundary, with its intensity governed by the loading direction, shear modulus ratio, and inhomogeneity shape. In addition, the maximum curvature of the inhomogeneity boundary can serve as an effective geometric indicator for evaluating the severity of stress concentration.