Adhesion enhancement in a dimpled surface with axisymmetric waviness and rate-dependent work of adhesion

Surfaces showing macroscopic adhesion are rare in industry but are abundant in Nature. Adhesion enhancement has been discussed mostly with geometrical systems (e.g. patterned surfaces), more rarely with viscoelasticity, and has the goal of increasing hysteresis and the detachment force at separation. Soft materials are common, and these have viscoelastic properties that result in a rate-dependent increase in toughness. Here the detachment of two half-spaces is studied, one being flat and the other having a dimple in the limit of short-range adhesion and rate-dependent work of adhesion, in the presence of axisymmetric single-scale waviness, which itself results in adhesion enhancement, similarly to the Guduru model of rough spheres. The dimpled surface shows pressure-sensitive adhesion, and when waviness is added, the roughness-induced toughening is enhanced. It is shown that when a rate-dependent work of adhesion is also accounted for, as in the present paper, assuming a power-law dependence of the effective work of adhesion on the crack tip velocity, the two enhancements are not completely multiplicative, as the "viscoelastic" one tends to prevail and indicates a new avenue of research for pressure-sensitive adhesion.