A quasistatic viscoelastic contact problem with friction

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. (C) 2000 Elsevier Science Ltd. All rights reserved.