Abstract:We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.
Keywords: viscoelastic materials, adhesion, Tresca's friction, fixed point, weak solution
AMS Subject Classification: 47J20 49J40 74M10 74M15