Weak formulations and solution multiplicity of equilibrium configurations with Coulomb friction

Mihai Bostan (1) , Patrick Hild (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

This work is concerned with the equilibrium configurations of elastic structures in contact with Coulomb friction. We obtain a variational formulation of this equilibrium problem. Then we propose sufficient conditions for the existence of an infinity of equilibrium configurations with arbitrary small friction coefficients. We illustrate the result in two space dimensions with a simple example.

Mots clés: Coulomb friction; linear elasticity; equilibrium configurations; weak formulations; continuum of solutions

Domaines: Equations aux dérivées partielles [math.AP]

Mihai Bostan, Patrick Hild. Weak formulations and solution multiplicity of equilibrium configurations with Coulomb friction. Mathematical Modelling of Natural Phenomena, 2009, 4 (1), pp.147-162. ⟨10.1051/mmnp/20094107⟩. ⟨hal-00466472⟩