Dynamics of wrinkling in ultrathin elastic sheets

TL;DR

This paper explores the dynamic wrinkling behavior of ultrathin elastic sheets impacted by a solid sphere, revealing how fluid inertia influences wrinkle coarsening and introduces a new dynamic stiffness controlling wrinkle wavelength.

Contribution

It introduces the concept of dynamic wrinkling driven by impact, highlighting the role of fluid inertia and dynamic stiffness in wrinkle pattern evolution, which differs from static models.

Findings

Dynamic wrinkling differs qualitatively from static wrinkling.

Fluid inertia inhibits wrinkle coarsening.

Dynamic stiffness controls wrinkle wavelength.

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 ultra-thin polymer sheet floating on water. The vertical deflection of the sheet's centre induced by impact draws material radially inwards, 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 quasi-static 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 new controls of wrinkle wavelength.