Analysis of a contact adhesive problem with normal compliance and nonlocal friction
Tom 104 / 2012
Annales Polonici Mathematici 104 (2012), 175-188 MSC: 74H20, 74M15, 74M10, 49J40, 35J87. DOI: 10.4064/ap104-2-5
The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result under a smallness assumption on the friction coefficient by using arguments of time-dependent variational inequalities, differential equations and the Banach fixed-point theorem.