This study is concerned with continuum models and numerical methods for wear, frictional heat and damage. Of special interest are so called fretting phenomena. Fretting occurs when two bodies in contact experience small periodic, relative motion which leads to wear and the promoted initiation of fatigue cracks. The work presented here is a part of a general attempt to give this phenomenon a continuum mechanical description suitable for numerical treatment.

The study consists of two main contributions concerning (i) the numerical treatment of a thermoelastic wear model and (ii) the formulation of a model of damage coupled to wear, regarded as a first attempt to develop a continuum model in order to study the crack initiation phase in fretting fatigue. The thesis consists of four papers.

Paper I concerns the numerical treatment of thermoelastic wear problems. Two different approaches, both utilizing a non-smooth Newton method as non-linear equation solver, are outlined and compared. Furthermore, the behaviour of the thermoelastic wear model is discussed based on the solution of two numerical examples.

Paper II is an review of some general observations regarding crack initiation in fretting and a survey of existing models and methods for predicting fretting fatigue failures.

Paper III is a literature survey concerning various methods to avoid mesh-dependency in connection with numerical solution of models exhibiting strain-softening with special emphasis on continuum damage mechanics.

Paper IV presents a model of damage coupled to wear. The model is based on a continuum damage model including the gradient of the damage variable.