Scale invariance of the contact mechanics of micropatterned elastic substrates

This paper describes the conditions for contact formation between soft elastic hemispheres and softelastic substrates micropatterned with pillars. These microstructured substrates were often proposed inthe two past decades for the control of adhesion. In this study the hexagonal micropillars are arranged inhexagonal arrays and the width L of the pillars as well as the distance D between the pillars (with L¼Dfor a sample) are both varied from one sample to another in order to keep the overall planar surfacefraction of the pillars constant. Additionally, two pillars of heights h¼4 mm and h¼16 mm are consideredhere. As expected from previous studies different contact morphologies are found as a function of theaspect ratio and the contact pressure. The contact may be formed (i) only at the top of the pillar, (ii) bothat the top and between the pillars, or (iii) simultaneously at the top of the pillars and in between thepillars at the centre of the contact for which the pressure is the highest. Unexpectedly it is shown in thislast case that the same contact morphology is obtained with the same pressure if the surface patternaspect ratio L/h is varied homothetically, suggesting a scale invariant behaviour of the contact formationbetween the hemisphere and the soft elastic micropatterned substrate.& 2013 Elsevier Ltd. All rights reserved.