Evolving wrinkles: time-dependent buckling of an elastic sheet on a liquid substrate

Source abstract

Abstract We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical set-up in the study of wrinkling, and while its static equilibrium configuration is well characterized, its dynamics are not. Here, we focus on modelling the transition from early-time, inertia-dominated wrinkle growth to late-time gravity-moderated equilibrium. For an initially flat sheet, an initial disturbance will first grow at the shortest available wavelengths, because this requires the least kinetic energy, but will subsequently transition to a longer preferred wavelength that minimizes potential energy. We observe that the evolving wave pattern must be a spectrum, as opposed to a fundamental wrinkle mode whose wavelength evolves in time. Our results demonstrate that changes in the dominant wrinkle wavelength are coupled to a decay in the compressive force, which is to be expected from equilibrium theory. As part of this study, we found that the system must have a dissipation mechanism in order to evolve into an equilibrium steady state. The dominant wrinkle wavelength and compressive force appear to be independent of the level of dissipation, although it does influence the shape of the wrinkle wave packet, with the spectrum narrowing as dissipation increases.