The present thesis concerns the thermomechanical modelling of contact, friction and wear. Within a framework of continuum thermodynamics, Signorini's contact conditions, Coulomb's law of friction and Archard's law of wear are derived by means of a free energy and a dissipation potential. The derivation is performed by defining a certain internal state variable which measures the wear gap. The free energy and the dissipation potential taken together constitute a generalized standard material for tribological systems.
This particular generalized standard material is studied in a one point contact problem. Existence and uniqueness of solutions to the so-called rate problem are investigated. A condition for existence and uniqueness of solutions is established, depending on the stiffness coefficients, the coefficients of friction and wear, and the normal contact force.
The generalized standard material is also utilized to develop a finite element method for wear problems taking place between an elastic body and a rigid foundation. A system of discrete equations is derived from the governing equations by using finite element approximations in space, an implicit discretization rule in time and an approach of projections for the tribological laws. The system of equations derived, which can be associated to an augmented Lagrangian, is solved for two- and three-dimensional problems using a Bouligand differentiable Newton method. In particular, the evolution of the contact stresses and the wear gaps are solved for a number of different fretting problems. It is studied how the contact stresses depend on the removal of material due to wear. Numerical results show that large values and large gradients in the contact stresses are developed in the region between stick and slip.
Furthermore, the Newton method is compared to an interior point method. An extensive comparison between these two methods is performed for two-dimensional friction problems. Numerically, it is found that the Newton method is superior in speed as well as in robustness.
Finally, a finite element method for two-dimensional thermoelastic wear problems is suggested. Following the ideas discussed above, a Newton method for a thermoelastic body, constrained by a rigid flat moving foundation, is given. This method is used to study the dependence between wear and frictional heat generation.