Dynamics of wrinkling in ultrathin elastic sheets

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.