An elliptical compressible liquid inclusion in an infinite nonlinearly coupled thermoelectric matrix

Abstract

We study the plane strain problem associated with an elliptical thermoelectrically insulated and compressible liquid inclusion embedded in an infinite homogeneous and isotropic nonlinearly coupled thermoelectric matrix under uniform remote electric current density and energy flux. With the aid of conformal mapping and analytic continuation, an exact closed-form solution to the problem is derived. In particular, an elementary expression for the internal uniform hydrostatic tension within the compressible liquid inclusion is obtained. Our result shows that the internal uniform hydrostatic tension is unaffected by the remote energy flux and is proportional to the square of the two components of the remote electric current density vector. Also presented is the hoop stress distribution along the elliptical interface on the matrix side.

Keywords:

• Analytic continuation
• compressible liquid inclusion
• conformal mapping
• hoop stress
• internal uniform hydrostatic tension
• thermoelectric material

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN-2023-03227 Schiavo).