Contact problems involving friction

Abstract

The Coulomb friction law is simple to apply in the formulation of elastic contact problems, but it is also a rich source of unexpected physical phenomena, including ranges of unstable dynamic response, history-dependence, ‘wedging’ and mathematical problems of existence and uniqueness of solution. We first explore the implications of the law in the context of simple discrete systems and demonstrate the importance of interaction [coupling] between the normal and tangential contact problems, particularly in problems of periodic loading. The discussion is then extended to problems of the elastic continuum, and to cases where elastodynamic effects must be included [for example, the interaction of a seismic disturbance with a frictional interface]. It is shown that finite element formulations of elastodynamic problems with Coulomb friction are inherently ill-posed and alternative friction laws that avoid this difficulty are discussed.