Scale invariance of the contact mechanics of micropatterned elastic substrates

This paper describes the conditions for contact formation between soft elastic hemispheres and soft elastic substrates micropatterned with pillars. These microstructured substrates were often proposed in the two past decades for the control of adhesion. In this study the hexagonal micropillars are arranged in hexagonal arrays and the width L of the pillars as well as the distance D between the pillars (with L=D for a sample) are both varied from one sample to another in order to keep the overall planar surface fraction of the pillars constant. Additionally, two pillars of heights h=4 µm and h=16 µm are considered here. As expected from previous studies different contact morphologies are found as a function of the aspect ratio and the contact pressure. The contact may be formed (i) only at the top of the pillar, (ii) both at the top and between the pillars, or (iii) simultaneously at the top of the pillars and in between the pillars at the centre of the contact for which the pressure is the highest. Unexpectedly it is shown in this last case that the same contact morphology is obtained with the same pressure if the surface pattern aspect ratio L/h is varied homothetically, suggesting a scale invariant behaviour of the contact formation between the hemisphere and the soft elastic micropatterned substrate.