A partially debonded circular elastic inhomogeneity with a liquid slit inclusion occupying the debonded section under uniform heat flux and temperature change

We study the two-dimensional heat conduction and thermoelastic problems associated with a circular isotropic elastic inhomogeneity partially debonded from an infinite isotropic elastic matrix subjected to uniform remote in-plane heat flux and uniform temperature change. The debonded portion of the circular interface is occupied by a thermally insulated and incompressible liquid slit inclusion. Closed-form solutions to the two problems are derived by solving two Riemann-Hilbert problems with discontinuous coefficients. The two unknown constants appearing in the solution of the thermoelastic problem are determined by imposing the incompressibility condition of the liquid inclusion. Elementary expressions for the internal uniform hydrostatic stress field within the liquid slit inclusion, the average mean stress within the circular elastic inhomogeneity, the rigid body rotation at the center of the circular inhomogeneity and the two complex stress intensity factors at the two tips of the debonded portion are obtained. A uniform temperature change will not induce any singular stress field and the entire circular interface remains perfect.