Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity. (English) Zbl 1059.74042

Hild, Patrick

Q. J. Mech. Appl. Math. 57, No. 2, 225-235 (2004).

Summary: This work is concerned with Coulomb friction model in continuum linear elastostatics. We consider the two-dimensional problem, and we recall that an infinity of solutions corresponding to slip may exist when the friction coefficient (or its opposite value) is an eigenvalue of a specific problem. We show that such coefficients exist, and we determine them explicitly for a simple class of problems. Finally, we exhibit cases in which the static friction problem admits an infinity of solutions slipping in the same direction.

MSC:

74M10	Friction in solid mechanics
74B05	Classical linear elasticity
74G35	Multiplicity of solutions of equilibrium problems in solid mechanics

Keywords:

eigenvalue