Thermoelectric and stress distributions around a smooth cavity in thermoelectric material

TL;DR

This paper derives exact analytical solutions for thermoelectric and stress distributions around cavities in thermoelectric materials, revealing how cavity shape and loading direction influence stress concentration and electric field distribution.

Contribution

It introduces a novel method to obtain explicit, finite-form solutions for thermoelectric problems with cavities, considering complex cavity shapes characterized by Laurent polynomials.

Findings

Stress and electric field distributions depend on cavity shape and loading direction.

Maximum stress and thermoelectric concentration occur near high curvature points.

Symmetrical cavity tips show extremum behavior when loading aligns with symmetry axes.

Abstract

Thermoelectric materials have attracted more and more attention since they are friendly to the environment and have potentials for sustainable and renewable energy applications. As typically brittle semiconductors with low mechanical strength and always subjected to defects and damages, to clarify the stress concentration is very important in the design and implement of thermoelectric devices. The two-dimensional thermoelectric coupling problem due to a cavity embedded in an infinite isotropic homogeneous thermoelectric material, subjected to uniform electric current density or uniform energy flux, is studied, where the shape of the cavity is characterized by the Laurent polynomial, and the electric insulated and adiabatic boundary around the cavity are considered. The explicit analytic solutions of Kolosov-Muskhelishvili (K-M) potentials and rigid-body translation are carried out through a novel tactic. Comparing with the reported results, the new obtained are completely exact and possess a finite form. Some results of three typical cavities are presented to analyze the electric current densities (energy fluxes) and stresses around the tips. The main conclusions include: the distribution of thermoelectric field and stress at the tip obviously depends on the curvature of the contour and loading directions; for triangle and square with symmetrical tips, the maximum thermoelectric and stress concentration reach the maximum or minimum when the loading direction is parallel to or perpendicular to the symmetry axis of the tip, which is distinct to the extremum characteristics of pentagram with bimodal of curvature around the tip; the maximum thermoelectric and stress concentration appear near the maximum curvature point for most load directions, but not at the maximum curvature point.