Thermoelastic contact has long been an important topic both in the solid mechanics and tribology. Contact is a principal method of applying loads to deformable bodies, and heat transfer often occurs during this contact due to frictional heating or a temperature difference. With the rapid increase in the use of anisotropic materials, the demand for methods and formulations to solve the thermoelastic contact problem for anisotropic materials has become increasingly urgent. In this dissertation, the thermoelastic contact for both isotropic and anisotropic materials is studied.

For isotropic materials, a two-dimensional thermoelastic rough surface contact model is derived which yields improved results than current models available in the literature. Also, the three-dimensional problem of a elastic half-space subjected to uniform heat flow over a rectangular area on the surface is considered and the results have potential use in many other problems such as boundary element formulations or the development of three-dimensional thermoelastic rough surface contact models.

For anisotropic materials, using the Stroh’s formalism, a two-dimensional rough surface contact model is derived which can be used as a tool in the analysis of anisotropic surfaces. In addition, the problem of thermoelastic contact on an anisotropic half-space is studied in detail, and general solutions for different types of thermal and mechanical boundary conditions are presented. As a direct application, the contact problem of a heated flat punch on an anisotropic half-plane is solved. Also, the contact problem of a single anisotropic strip subjected to tractions on its boundaries is considered, and an approximate solution for certain types of anisotropic materials is proposed.