Response of frictional receding contact problems to cyclic loading

Dundurs [Properties of elastic bodies in contact. In: de Pater AD, Kalker JJ, editors. The mechanics of the contact between deformable bodies. Delft: Delft University Press; 1975. p. 54–66] has shown that if the contact area in a frictionless elastic system under load is equal to or smaller than that before loading (i.e. the contact is receding), the extent of the contact area is load-independent and the stress field varies linearly with load. Similar results apply to problems with Coulomb friction as long as the loading is monotonic, but otherwise non-linearities and variation in the contact area occur. In this paper, we examine this effect for the simple case of an elastic block pressed against a frictional rigid plane. During unloading there is continuous variation of both contact and slip/stick boundaries. For the important case where the loading contains a mean and a periodic component, the system approaches a steady periodic state relatively slowly and in this final state there is continuous variation of the contact area, with the minimum (i.e. the maximum amount of separation) occurring at the minimum applied load.