Understanding Nanostructured Topography on Flower Petals: Hierarchical Wrinkles in Soft Multilayers

Hierarchical wrinkles on flower petals enable unique iridescence to attract pollinators. Although similar patterns have been observed on graded elastomers, mimesis of the natural patterns and relative dimensions with a controllable and tunable manner is challenging. Inspired by the multiple-layered structure of petal skins, here we present a physical model and a corresponding numerical model based on three-layered thin films. The layer-by-layer integration provides accuracy in controlling thickness and mechanical properties of thin films, thus enabling quantitative relations between physical and numerical models. We quantify the sequential development of a hierarchical structure, consisting of small wrinkles coupled with larger sinusoidal deformations. We found their wavelength follows the bilayer wrinkling theory; whereas the amplitudes of small wrinkles have a systematic spatial distribution largely controlled by larger wrinkles. We also discovered a collapse from the dual-wrinkling mode to a single-wrinkling mode, which depends upon thickness and mechanical properties of top layers. A phase map of the two wrinkling modes is constructed to guide the design of hierarchical wrinkles.