Perturbation of the elastic and thermoelectric fields caused by a rigid inclusion in a thermo-electro-elastic full plane

Abstract

The two-dimensional thermoelectric coupling problem of a rigid inclusion embedded in a thermoelectric material subjected to uniform electric current density or uniform energy flux at infinity is studied, where the electric insulated and adiabatic properties on the boundary of the rigid inclusion are considered. Compared with previous reports, the explicit and analytic solutions of Kolosov-Muskhelishvili (K-M) potentials in a compact form are obtained when the shape of rigid inclusion is described by Laurent polynomial with finite N terms, and the rigid-body displacement of the rigid inclusion relative to the matrix is considered to make the boundary constraints exactly satisfied. The rigid-body displacement, thermoelectric field and stress around the boundary are analyzed. The results show that the rigid-body displacements caused by the uniform electric current density or uniform energy flux applied alone at infinity have different distributions; as the load direction changes, the electric current density (energy flux) and stress on the boundary are periodically distributed along the direction of obtaining the maximum value, and the maximum thermoelectric concentration and stress concentration happen in different load directions.