ABSTRACT
In this chapter we consider a general viscoelastic body in adhesive contact with a reactive foundation, in the case when the external forces vary slowly and the quasistatic approximation is valid. The evolution of the bonding field is described by a first-order ordinary differential equation. We derive a variational formulation of the problem and prove the existence of its unique solution. The proof is based on the construction of two intermediate problems for the displacement field and for the bonding field. We prove the unique solvability of the intermediate problems, then we construct a contraction mapping whose unique fixed point is the weak solution of the original problem. The continuous dependence of the solution on the bonding parameters is also studied. Semidiscrete and fully discrete schemes for the problem are described and error estimates obtained.
