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 t he quasi-static Signorini problem with Coulomb friction should hold, provid ed that the friction coefficient is lower than a critical value. Recently, the existence of solutions to the quasi-static Signorini problem with non-l ocal 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 u niqueness does not hold, in general, for an arbitrarily small friction coef ficient. (C) 1998 Elsevier Science Ltd. All rights reserved.