Role of viscoelasticity in the adhesion of mushroom-shaped pillars

Abstract: Mushroom-shaped pillars have been extensively studied for their superior adhesive properties, often drawing inspiration from natural attachment systems observed in insects. Typically, pillars are modeled with linear elastic materials in the literature; in reality, the soft materials used for their fabrication exhibit a rate-dependent constitutive behavior. This study investigates the role of viscoelasticity in the adhesion between a mushroom-shaped pillar and a rigid flat countersurface. Interactions at the interface are assumed to be governed by van der Waals forces, and the material is modeled using a standard linear solid model. Normal push and release contact cycles are simulated at different approaching and retracting speeds. Results reveal that, in the presence of an interfacial defect, a monotonically increasing trend in the pull-off force with pulling speed is observed, and the corresponding change in the contact pressure distribution suggests a transition from short-range to long-range adhesion. This phenomenon corroborates recent experimental and theoretical investigations. Moreover, the pull-off force remains invariant to the loading history, due to our assumption of a flat-flat contact interface. Conversely, in absence of defects, detachment occurs after reaching the theoretical contact strength, and the corresponding pull-off force is found to be rate independent.