This study presents a semi-analytical solution for the adhesive contact between a rigid sphere and an array of viscoelastic fibrils, modeling interactions which are commonly encountered in biological adhesion and engineered surfaces. The viscoelastic behavior of the fibrils is modelled using a standard viscoelastic solid (SVS) model, capturing both elastic and time-dependent deformation responses. The contact problem is formulated by considering the normal approach of the rigid sphere onto the fibrillar surface, dominated by a harmonic displacement law, and implementing different adhesive contact criteria. The analysis provides the pull-off force as function of the vibrations’ frequency and amplitude, also highlighting the dependence from the material parameters and providing insights into vibrating detachment processes.
Califano et al. (2026) studied this question.