A solution of the elliptic piezoelectric inclusion problem under uniform heat flux

Abstract

An analytical solution to the problem of an elliptic piezoelectric inclusion embedded in an infinite matrix with different thermal/elastic/electric properties under a uniform heat flow at infinity is presented by employing the complex variable method in assistance with the techniques of conformal mapping and analytical continuation. First, the holomorphic functions characterizing the thermal/elastic/electrical fields are obtained, then expressions are derived for the heat flow, stress and electric displacement in the inclusion, along the interface and in the matrix. It is shown that a uniform heat flow at infinity induces a linear stress and electric displacement distribution within the inclusion. The final numerical example demonstrates that continuity conditions at the interface are indeed satisfied and shows the effects of material mismatch between the two phases.