Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets

TL;DR

This paper investigates how the geometry and thermal fluctuations influence tilt transitions in elastic sheets, revealing that aspect ratio, not temperature alone, primarily controls the transition dynamics.

Contribution

It introduces a geometric control framework for tilt transition dynamics in thermalized elastic sheets, combining mean-field theory and simulations to identify key parameters.

Findings

Transition rate depends on aspect ratio and temperature.

Thermal fluctuations can suppress tilt inversion.

Robustness of the tilted state increases with thermal effects.

Abstract

We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane above or below the horizontal. The resultant thermally roughened two-state (up/down) system possesses rich dynamics on multiple time scales. In the tilted regime, a finite energy barrier separates the spontaneously chosen up state from the inversion-symmetric down state. Molecular dynamics simulations confirm that over a sufficiently long time, such thermalized elastic sheets transition between the two states, residing in each for a finite dwell time. One might expect that temperature is the primary driver for tilt inversion. We find, instead, that the primary control parameter, at fixed tilt order parameter, is the dimensionless and purely geometrical aspect ratio of the clamped width to the total length of the otherwise-free sheet. Using a combination of an effective mean-field theory and Kramers' theory, we derive the transition rate and examine its asymptotic behavior. At length scales beyond a material-dependent thermal length scale, renormalization of the elastic constants qualitatively modifies the temperature response. In particular, the transition is suppressed by thermal fluctuations, enhancing the robustness of the tilted state. We check and supplement these findings with further molecular dynamics simulations for a range of aspect ratios and temperatures.