Adhesive contact of a viscoelastic fibrillar surface — A homogenized model

A 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.