Surface buckling with deterministic peaks/valleys regulated by bio-inspired micro-structures periodically distributed on elastic bilayers

Abstract

Surface buckling for film/substrate systems has an extensive application in flexible electronics, microfluidics, and adhesives. The location of the peaks and valleys, however, is still unpredictable due to its strong dependency upon external perturbations and the inevitable edge effects. Inspired by the sharp spines on ribbed stems of an echinopsis cactus, periodic surface micro-structures, including pyramidal intaglios and pyramidal reliefs, are adopted to tune the buckling experimentally and numerically. Although the instability patterns in our research are similar to those regulated by the stiff film pattern geometry, the wavelengths are nearly uniform in the whole area without obvious edge effects in the position of the surface micro-structures. The number of the wrinkle-like patterns between two micro-structures is equal to n when the width of the normalized center to center distance d¯ is in a range of about n−0.4 to n+0.6. More importantly, the pyramidal intaglios and pyramidal reliefs have well-regulated but opposite locations in different instability patterns, which means that the peaks and valleys are predictable upon the surface buckling. The deterministic peaks/valleys of the surface instability regulated by micro-structures provides a worthy guidance on the topography design, such as the distribution of the functional components in stretchable electronics based on structural designs.