A counter-example to uniqueness in quasi-static elastic contact problems with small friction

It is often conjectured that the existence and uniqueness of solutions to the quasi-static Signorini problem with Coulomb friction should hold, provided that the friction coefficient is lower than a critical value. Recently, the existence of solutions to the quasi-static Signorini problem with non-local Coulomb friction was shown (M. Cocu, E. Pratt, M. Raous, Int. J. Engng. Sci. 34 (1996) 783-798) in functional spaces of type W-1.p(0, T) and for a sufficiently low friction coefficient. In this paper, it is proved that uniqueness does not hold, in general, for an arbitrarily small friction coefficient. (C) 1998 Elsevier Science Ltd. All rights reserved.