Role of viscoelasticity in the adhesion of mushroom-shaped pillars

The contact behaviour of mushroom-shaped pillars has been extensively studied for their superior adhesive properties, often inspired by 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 behaviour. Additionally, conventional models focus solely on the detachment phase of the pillar, overlooking the analysis of the attachment phase. As a result, they are unable to estimate the energy loss during a complete loading-unloading cycle. 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. The corresponding change in the contact pressure distribution suggests a transition from short-range to long-range adhesion, corroborating 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 the absence of defects and under the parameters used in this study, detachment occurs after reaching the theoretical contact strength, and the corresponding pull-off force is found to be rate independent. Notably, the hysteretic loss exhibits a peak at intermediate detachment speeds, where viscous dissipation occurs, which holds true in both the presence and absence of a defect. However, the presence of a defect shifts the region where the majority of viscous dissipation takes place.