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

TL;DR

This paper models the dynamic evolution of wrinkles in a floating elastic sheet under compression, revealing how initial short wavelengths transition to longer ones as the system approaches equilibrium, highlighting the interplay of inertia and gravity.

Contribution

It introduces a time-dependent model capturing the transition from initial inertia-driven wrinkle growth to gravity-influenced equilibrium in floating elastic sheets.

Findings

Initial disturbance grows at shortest wavelengths due to minimal kinetic energy

Wavelength transitions to longer values to minimize potential energy

Dominant wrinkle wavelength change correlates with decay in compressive force

Abstract

We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical setup in the study of wrinkling, and whilst its static equilibrium configuration is well characterised, its dynamics are not. In this work, we focus on modelling the transition from early, inertia-dominated wrinkle growth to late-time gravity-moderated equilibrium. For an initial configuration in which the sheet is flat, 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 minimises 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.