A uniqueness criterion for the Signorini problem with Coulomb friction. (English) Zbl 1194.74225

Renard, Y.

Wriggers, Peter (ed.) et al., Analysis and simulation of contact problems. Papers based on the presentation at the 4th contact mechanics international symposium (CMIS 2005), Loccum, Germany, July 4–6, 2005. Berlin: Springer (ISBN 3-540-31760-0/hbk). Lecture Notes in Applied and Computational Mechanics 27, 161-169 (2006).

Summary: Some optimal a priori estimates are given for the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem) and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have been presented in the continuous framework. It is proven, here, that if a solutions satisfies an hypothesis on the tangential displacement and if the friction coefficient is small enough, it is the unique solution to the problem.
For the entire collection see [Zbl 1089.74008].

MSC:

74M15	Contact in solid mechanics
74M10	Friction in solid mechanics
74G30	Uniqueness of solutions of equilibrium problems in solid mechanics