We extend the study [1] devoted to the dynamic response of a structure made of two linearly elastic bodies connected by a thin soft adhesive layer made of a Kelvin Voigt type nonlinear viscoelastic material to the case of a Generalized Standard Material with a positive definite quadratic density of free energy. A concise formulation in terms of an evolution equation in a Hilbert space of possible states with finite energy makes it possible to identify the asymptotic behavior, when some geometrical and mechanical parameters tend to their natural limits, like the response of the two bodies connected by a mechanical constraint. Its law has the same structure as that of the adhesive but with coefficients accounting for the relative behavior of the parameters.