Thermal Green’s functions in plane anisotropic bimaterials with spring-type and Kapitza-type imperfect interface

Abstract

By means of the extended version of the Stroh formalism for uncoupled thermo-anisotropic elasticity, two-dimensional Green’s function solutions in terms of exponential integrals are derived for the thermoelastic problem of a line heat source and a temperature dislocation near an imperfect interface between two different anisotropic half-planes with different thermo-mechanical properties. The imperfect interface investigated here is modeled as a generalized spring layer with vanishing thickness: (1) the normal heat flux is continuous at the interface, whereas the temperature field undergoes a discontinuity which is proportional to the normal heat flux; (2) the tractions are continuous across the interface, whereas the displacements undergo jumps which are proportional to the interface tractions. This kind of imperfect interface can be termed a thermally weakly conducting and mechanically compliant interface. In the Appendix we also present the isothermal Green’s functions in anisotropic bimaterials with an elastically stiff interface to demonstrate the basic ingredients in the analyses of a stiff interface.