An imperfectly bonded elliptical inhomogeneity under uniform heat flux and uniform temperature change

We consider the uncoupled two-dimensional steady-state heat conduction and thermoelastic problems associated with an elliptical isotropic elastic inhomogeneity imperfectly bonded to an infinite isotropic elastic matrix subjected to uniform remote heat flux and uniform temperature change. The imperfect interface is weakly conducting in heat conduction and spring-type in elasticity, and is characterized by two non-negative imperfect interface functions. The same degree of imperfection in elasticity is realized in both the normal and tangential directions of the elliptical interface. When the two interface functions are judiciously chosen, a uniform heat flux will induce a linear stress distribution within the elliptical inhomogeneity and a uniform temperature change will induce a constant stress distribution within the inhomogeneity. Explicit closed-form expressions for the temperature and thermoelastic fields in the elliptical inhomogeneity and the matrix are obtained.