  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.
