Geometrical Control of the Tilt Transition in Single-Clamped Thermalized Elastic Sheets

We study the dynamics of the tilt transition of thermalized thin elastic sheets clamped at one end only in the manner of a cantilever. Beyond a critical strain, such a sheet undergoes a tilt transition with a finite energy barrier separating the spontaneously chosen tilt plane (up) from its oppositely oriented state (down). The finite barrier implies that, over long time scales, the elastic sheet may transition between the two states, residing in each for a finite time. Naively, temperature might be assumed as the primary driver for these transitions, but we find that geometric characteristics, in particular the aspect ratio of the sheet, is the key controller of the transition probability. Using a combination of an effective mean field elastic theory and transition-state theory, we derive an expression for the rate of transition between the two tilted states. We show that, at scales larger than a thermal length scale, renormalization of the elastic constants weakens the temperature dependence and allows for geometrical factors to dominate.