Rate-dependent adhesion of viscoelastic contacts. Part II: Numerical model and hysteresis dissipation

In this paper, we propose a numerical model to describe the adhesive normal contact between a glass spherical indenter and a viscoelastic model rough substrate of PDMS material. The model accounts for dissipative process under the assumption that viscoelastic losses are localized at the (micro)-contact lines. Numerical predictions are then compared with experimental measurements, which show a strong adhesion hysteresis mostly due to viscous dissipation occurring during pull-off. This hysteresis is satisfactorily described by the contact model which allows to distinguish the energy loss due to material dissipation from the adhesion hysteresis due to elastic instability. Our analysis shows that the pull-off force required to detach the surfaces is strongly influenced by the detachment rate and the root mean square (rms) roughness amplitude, but it is almost unaffected by the maximum load from which unloading starts. Moreover, the increase in the length of the boundary line separating contact and non-contact regions, which is observed when moving from smooth to rough contacts, negligibly affects the viscous dissipation. Such increase is much less significant than the reduction in contact area, which therefore is the main parameter governing the strong decrease in the effective surface energy for the specific rough geometry considered in the present work.