A QUASISTATIC UNILATERAL CONTACT PROBLEM WITH NORMAL COMPLIANCE AND NONLOCAL FRICTION

We consider a mathematical model which describes the quasistatic unilateral and frictional contact of a linear elastic body with a foundation. The contact is modelled with a normal compliance condition of such a type that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We present the classical formulation of the problem, the variational formulation and establish the existence of a weak solution, when the coefficient of friction is sufficiently small. The proofs are based on arguments of time-discretization, compactness and lower semicontinuity.