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We consider a mathematical model which describes the quasistatic frictional contact between a viscoelastic body with long memory and a foundation.The contact is modelled with a normal compliance condition in such a way that the penetration is limited and restricted to unilateral constraint and associated to the nonlocal friction law with adhesion, where the coefficient of friction is solution-independent. The bonding field is described by a first order differential equation. We derive a variational formulation written as the coupling between a variational inequality and a differential equation. The existence and uniqueness result of the weak solution under a smallness assumption on the coefficient of friction is established. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.

Mathematics Subject Classification (2010): 54AXX.

Keywords: Viscoelastic, normal compliance, adhesion, friction, variational inequality, weak solution.