Analysis of inclusion in thermoelectric materials: The thermal stress field and the effect of inclusion on thermoelectric properties

This paper analyses a two-dimensional problem in thermoelectric materials with an inclined elliptic inclusion. We have obtained the closed-form solutions of electric current density and temperature considering the inclusion's electrical and thermal permeability. Based on the derived thermoelectric field, the thermal stresses are given in the explicit form and the effect of inclusion on effective thermoelectric properties is investigated. The electrically impermeable and thermally impermeable inclusions will respectively cause maximum electric current concentration and heat concentration. The thermally impermeable and rigid inclusion will cause maximum stress concentration around the inclusion. Furthermore, we find that the effective electric conductivity (effective thermal conductivity) of the matrix-inclusion system is increased when the inclusion have higher electric conductivity (thermal conductivity) than the matrix. It is possible to enhance the effective figure of merit by inserting inclusions with specific electric conductivity and heat conductivity. It predicts a new way for the design of high-performance thermoelectric devices. The results in this paper can be directly used for reliability consideration in design and optimization of thermoelectric devices in engineering.