Stability of thermoelastic contact.

Abstract

When heat is conducted across an interface between two different materials, the interaction between thermoelastic distortion and thermal contact resistance can cause the system to behave in many interesting ways, one of them being the non-existence of steady-state solution if idealized boundary conditions are applied. Attempts to overcome this difficulty prompted the assumption of a pressure or gap dependent thermal resistance across the interface. However, multiple solutions are still possible with such more realistic boundary conditions. This thesis extends the scope of investigations on uniqueness and stability of solutions to physically more complex thermoelastic contact systems. For the simple one-dimensional model, it is found that there is a range of conditions under which the steady-state solution is unique but unstable. A numerical study shows that under such conditions the system always tends to a steady oscillatory state. These conclusions have important implications for the classical steady-state solutions to two and three-dimensional thermoelastic contact problems. Since the uniqueness of such solutions cannot now be regarded as a guarantee of stability, their stability needs to be re-examined. In particular, we must accept the possibility that a steady oscillatory state exists. To verify these predictions, a two-dimensional system has been examined with particular attention on the influence of material properties on the stability criterion. It is found that most material combinations exhibit one or other of two kinds of stability behavior. A numerical method is then developed to study the long term behavior of such a system in detail. The results confirm the criterion developed in the analysis of the two half-plane system. Results have also reaffirmed some of the previously known behavior classes, but also exposed a new kind: when heat flows into the less distortive material, the transient solution can tend to a state in which a disturbance with contact and separation regions travels along the interface at constant speed while retaining the same form.