A variational inequality and applications to quasistatic problems with Coulomb friction

Abstract

The aim of this paper is to study an evolution variational inequality that generalizes some contact problems with Coulomb friction in small deformation elasticity. Using an incremental procedure, appropriate estimates and convergence properties of the discrete solutions, the existence of a continuous solution is proved. This abstract result is applied to quasistatic contact problems with a local Coulomb friction law for nonlinear Hencky and also for linearly elastic materials.

Keywords:

• Evolution inequalities
• existence results
• quasistatic problems
• nonlinear materials
• Coulomb friction

AMS Subject Classifications:

• 35Q74
• 49J40
• 74D10
• 74H20

Notes

No potential conflict of interest was reported by the author.