Modeling the soft backing layer thickness effect on adhesion of elastic microfiber arrays

A recent experiment has shown that the force required to pull off a flat circular rigid punch in adhesive contact with an array of elastic fibrils is sensitive to the thickness of the elastic backing layer to which these fibrils are attached. This result motivates Lis to study the effect of sample compliance on the adhesion of fibril arrays. A closed form expression for the compliance of such arrays attached to a backing layer of finite thickness is derived. Our model is based on the assumption that the adhesive strength of a fibril is deterministic. In addition, we show that the normalized pull-off force is inversely proportional to the square root of a single dimensionless parameter beta. For large beta, the pull-off force is low as it is governed by the stress concentration at the punch edge. For small beta, this pull-off force reaches a theoretical limit that is governed by the ability of fibrils to share load equally [equal load sharing (ELS) limit]. The pull-off force predicted by our model is compared with new experimental data. Our model shows the correct trend but underestimates the pull-off force in the ELS limit. The difference between our theoretical predictions and experimental results is attributed to alignment difficulties in the experiments and the fact that the adhesive strength of fibrils is governed by local statistics. (C) 2008 American Institute of Physics.