Thermoelectric and stress distributions around a smooth cavity in thermoelectric material

•In this paper the thermoelectric coupling problem of an infinite homogeneous isotropic thermoelectric material with a smooth cavity and exerting a uniform current density and/or uniform energy flux is studied.•New analytical solutions are completely exact, and operable for complex shapes.•New solutions have a finite form for cavity characterized by Laurent polynomial.•The curvature of the cavity contour affects the distribution of the fields.•The maximum stress concentration appears near the points with extremal curvature.