Argatov, I.I.ArgatovPapangelo, A.A.Papangelo2025-10-292025-10-292025-10-14Mechanics Research Communications 149: 104535 (2025)https://hdl.handle.net/11420/58333A fibrillar interface is modeled as a regular array of cylindrical micropillars bonded to a substrate, with a focus on the viscoelastic properties of the fibrils. A one-dimensional linear constitutive model describes the coupled deformation of an individual fibril and the substrate. For a compliant viscoelastic substrate, the interaction backing layer effect between fibrils through the substrate deformations is also accounted for. In the case of a viscoelastic Winkler-type foundation whose adhesive mechanism is described by the Shrimali–Lopez-Pamies criterion of maximum rate-independent elongation of the foundation elements, an exact analytical solution is derived for the displacement-controlled loading protocol. A leading-order discrete asymptotic model is developed for the Schapery-type rate-independent adhesive contact between the viscoelastic fibrillar substrate and a rigid punch. By neglecting the influence of the backing layer, a homogenized model is derived in detail. The debonding incubation time is introduced, and an analytical approximation for the pull-off force is obtained under conditions of strong adhesion and fast unloading after a long dwell time.en1873-39722025Elsevierhttps://creativecommons.org/licenses/by/4.0/Asymptotic modelFibrillar surfaceHomogenization approachPull-off forceRate-independent adhesionSchapery modelShrimali–Lopez–Pamies (SLP) modelViscoelastic contactTechnology::620: Engineering::620.1: Engineering Mechanics and Materials ScienceJournal Articlehttps://doi.org/10.15480/882.1605810.1016/j.mechrescom.2025.10453510.15480/882.16058Journal Article