Dynamics of wrinkling in ultrathin elastic sheets

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.

Mode Coarsening or Fracture: Energy Transfer Mechanisms in Dynamic Buckling of Rods

“…In fact, following an impact, the preferred wavelength of the buckling instability of rods (Fig. 1) is quite different from Euler's static buckling mode, and drives characteristic fragmentation patterns of brittle rods [11], or the timedependent wrinkling pattern of impacted sheets [12,13]. Yet, a wealth of questions remains when it comes to purely elastic dynamic buckling; that is, when no energy is dissipated by small scale thermal fluctuations [14], longrange viscous deformation [2], or abrupt fracture.…”

“…This difference means that the experimental mode coarsening mechanism occurs faster in time than predicted by the model suggesting that the energy transfer from high to lower wave numbers is accelerated by some form of energy dissipation. While viscous material dissipation mechanisms can be excluded (given the extreme short duration of the buckling experiment), we remind ourselves that the experiment did not take place in vacuum, but in air involving losses due to the drag of the deforming rod with the surrounding air, a phenomenon known to influence coarsening dynamics [7,13].…”

Dynamic Reversible Evolution of Wrinkles on Floating Polymer Films under Magnetic Control

“…Therefore, it is reasonable to say that this work is at least experimentally novel. Additionally, it is worthy to note that the dynamic and reversible evolution of surface wrinkles in our system causes no damage to the polymer film, and no hysteretic effect on the evolution process, which is fundamentally different from a steel ball impacting the floating film, and dripping a water droplet on the floating film [21,31].…”

“…This indentation depth results in the visual circular halo effect. Meanwhile, with the increase in magnetic force, the radial stress exerted on the film in the radial direction increased and further, the induced compressive stress in the circumferential direction synchronously increased, finally leading to a decrease in the wrinkle wavelength, and in turn, an increase in the wrinkle number [21]. Further increasing the distance between the magnet and the magnetic droplet to 7.457 mm, the circular halo expands outward, a small number of folds come out, and the wrinkle number decreases to 345 (Figure 2c,h).…”

“…When a steel ball is used to impact the floating film, it compresses the film downward, and further generates radial stress in the radial direction and compressive stress in the circumferential direction. In order to alleviate this compressive stress, radial wrinkles are triggered, and a series of surface morphologies evolve [21]. Additionally, loading by poking with a needle on the floating film has a similar wrinkling behavior as the impact of a steel ball.…”