Adhesive Contact of Visco-elastic Bodies and Defect Measures Arising by Vanishing Viscosity

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when delamination is in Mode II (pure shear). The solutions thus obtained involve certain defect-like measures recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity. Reflecting also the conventional engineering concept, the delamination is thus driven rather by stress than energy. An explicit example leading to a nontrivial defect measure is given.