The authors of this paper consider a viscoelastic body that is clamped onto one part of a boundary, is subject to a given surface traction on a second part of the boundary, and can come in contact with an obstacle on the third part of the boundary. The contact is subjected to an adhesion effect, whose evolution is described by an ordinary differential equation.

A variational formulation of this problem is derived, and unique solvability for the displacement, stress, and adhesion fields is established. The authors also consider a discretization scheme of the variational problem, and derive error estimates. The paper concludes with numerical results for a one- and a two-dimensional test problem.