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We perform a dimension reduction analysis for a coupledrate-dependent/rate-independent adhesive-contact model in the setting ofvisco-elastodynamic plates. We work with a weak solvability notion inspired bythe theory of (purely) rate-independent processes, and accordingly term therelated solutions `Semistable Energetic'. For Semistable Energetic solutions,the momentum balance holds in a variational sense, whereas the flow rule forthe adhesion parameter is replaced by a semi-stability condition coupled withan energy-dissipation inequality. Prior to addressing the dimension reductionanalysis, we show that Semistable Energetic solutions to the three-dimensionaldamped adhesive contact model converge, as the viscosity term tends to zero, tothree-dimensional Semistable Energetic solutions for the undamped correspondingsystem. We then perform a dimension reduction analysis, both in the case of avanishing viscosity tensor (leading, in the limit, to an undamped model), andin the complementary setting in which the damping is assumed to go to infinityas the thickness of the plate tends to zero. In both regimes, the presence ofadhesive contact yields a nontrivial coupling of the in-plane and out-of-planecontributions. In the undamped scenario we obtain in the limit anenergy-dissipation inequality and a semistability condition. In the dampedcase, instead, we achieve convergence to an enhanced notion of solution,fulfilling an energy-dissipation balance.

A coupled rate-dependent/rate-independent system for adhesive contact in Kirchhoff-Love plates