Bifurcations in contact problems with local Coulomb friction. (English) Zbl 1155.74032

Haslinger, J.; Kučera, Radek; Vlach, O.

Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 811-818 (2008).

Summary: This contribution illustrates the bifurcation behaviour of solutions to contact problems with local Coulomb friction. The bifurcation character of solutions is well-known for models with a low number of degrees of freedom. Our aim is to show that a similar phenomenon occurs when a finite element approximation with a high number of degrees of freedom is used. We experimentally find the critical value of the coefficient of friction for which one branch of solutions splits into two.
For the entire collection see [Zbl 1145.65001].

MSC:

74M15	Contact in solid mechanics
74M10	Friction in solid mechanics
74G60	Bifurcation and buckling
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

finite element approximation; critical coefficient of friction