Detachment of a rigid solid from an elastic wavy surface: Theory

The mechanics of detachment between a wavy elastic half space and a rigid solid is considered. Solutions for the axisymmetric problem of a rigid sphere and the plane strain problem of a rigid cylinder detaching from a wavy surface are developed. The interacting solids are taken to be in complete contact over a finite area initially. It is shown that the surface waviness makes the detachment process unstable, with the interface separating in alternating stable and unstable segments. Each unstable segment dissipates mechanical energy, leading to an increase in the total work of separation compared to that of a flat surface. Further, waviness causes the maximum separation force or the pull-off force to increase during detachment, resulting in an apparent toughening of the interface. This mechanism provides an alternative explanation to the experimental observations in the literature that roughness can sometimes lead to increase in pull-off force. It also illustrates the role of roughness in the attachment capability of several insect feet possessing soft pads. The basic solution presented here can be used to analyze the detachment of surfaces with multiple scale roughness as well. The solution also suggests strategies to improve reversible adhesion of a soft material by designing optimal surface topographies.