Dynamics of wrinkling in ultrathin elastic sheets

Significance

Elastic instabilities provide a means of generating regular topographies with a well-defined wavelength. For example, a thin elastic film attached to a softer substrate buckles into an array of regular wrinkles under quasistatic compression. The wrinkle wavelength is selected by the mechanical properties of the system so that different wavelengths are typically attained through variation of the film thickness. Here, we show that, for a film of given thickness, variation in the wrinkle wavelength can be achieved dynamically. Our study of impact-induced wrinkling demonstrates that the inertial response of the substrate results in an evolving wrinkle wavelength, opening the route toward dynamic tuning of wrinkle-patterned topographies.

Abstract

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic balance between the object’s bending stiffness and an effective substrate stiffness, which may originate from a true substrate stiffness or from tension and curvature along the wrinkles. Here, we investigate dynamic wrinkling induced by the impact of a solid sphere onto an ultrathin polymer sheet floating on water. The vertical deflection of the sheet’s center induced by impact draws material radially inward, resulting in an azimuthal compression that is relieved by the wrinkling of the entire sheet. We show that this wrinkling is truly dynamic, exhibiting features that are qualitatively different to those seen in quasistatic wrinkling experiments. Moreover, we show that the wrinkles coarsen dynamically because of the inhibiting effect of the fluid inertia. This dynamic coarsening can be understood heuristically as the result of a dynamic stiffness, which dominates the static stiffnesses reported thus far, and allows control of wrinkle wavelength.