Spatially and directionally controlled wrinkles and folds on a moduli-patterned 2D elastic substrate under compressive stresses

Abstract

Mechanical instabilities such as wrinkling or folding have long been known for one universal mecha-nism for the pattern formation in nature as a part of morphogenesis with various scales. These instabilities could be triggered when elastic materials are subjected to compressive stresses. In the laboratory level, these instability-induced patterns on a surface have been applied to various applications. Moreover, micro- and nanoscale instability-induced patterns have become new way to obtain novelty to existing devices or materials. However, these patterns have intrinsic randomness so that various applications have limited utilities. In this research, new strategy is suggested to control surface structures originated from mechanical instability under biaxial compressive stresses. To address relative strains, we constructed moduli-patterned elastic membranes using scrapping-mediated micromolding process. We observed that typical formations of wrinkles and folds are occurred only the softer region. By modifying the boundary conditions and geometry, we demonstrated control over the final morphology having spatiality and directionality on a two-dimensional space. Moreover, to confirm the strain localization behavior, we calculated strain distribution on a moduli-patterned substrate using a finite element analysis (FEA). The local strain in the softer region was always higher than a harder region, resulting in selective pattern formation by inducing proper strains with relative orientation and position between each structures. The ideas introduced here can be applied to various patterns depending on diverse purposes. Adjusted scattering through this controlled instability-induced patterns are demonstrated as a kind of optical applications. In conclusion, this controlled instability over the formation of spontaneously formed structures offers opportunities for fabricating surface with a complex, scalable, and optically functional micrometer and sub-micrometer scale patterns without the burden of costly lithographic procedures.