Abstract

We consider a mathematical model which describes the bilateral frictional contact of a viscoelastic body with an obstacle. The viscoelastic constitutive law is assumed to be nonlinear and the friction is described by a nonlocal version of Coulomb's law. A weak formulation of the model is presented and an existence and uniqueness result is established when the coefficient of friction is small. The proof is based on classical results for elliptic variational inequalities and fixed point arguments. We also consider a model for the wear of the contacting surface due to friction. In the case of sliding contact we obtain a new nonstandard contact boundary condition. We prove the existence of the unique weak solution to the problem with the same restriction on the friction coefficient.

Author Keywords: Nonlinear viscoelastic material; Bilateral contact; Nonlocal Coulomb's friction law; Variational inequality; Fixed point; Sliding contact; Archard's law; Wear

Article Outline

1. Introduction

2. Notation and preliminaries

3. Problem statement and variational formulation

4. Proof of Theorem 3.1

5. The problem with wear

Acknowledgements

References