Thermoelasticity and Contact

Thermoelastic deformations can have a significant effect on the contact between elastic bodies, particularly in cases where the thermal boundary conditions at the interface are influenced by the contact pressure. In the classical Hertzian problem, the size of the contact area depends on the magnitude and direction of heat flow between the bodies. Idealized thermal boundary conditions can lead to ill-posed steady-state problems, but this difficulty is resolved by assuming a pressure-dependent thermal contact resistance. Steady states of the system can be unstable even when they are unique, in which case the behavior is either oscillatory or involves the steady motion of a contact pressure wave along the interface. Analytical and numerical perturbation methods have been developed to investigate the stability problem. These results find applications in heat transfer processes involving solid-solid contact, including the solidification of castings. In brakes and clutches, the heat generated at the sliding interface causes thermal distortion leading to `̀ frictionally excited thermoelastic instability’ ’ or `̀ TEI,’’ in which contact becomes localized in `̀ hot spots’’ at the interface. Recent results enable us to make good predictions of the conditions under which this occurs.