Spontaneous tilt of single-clamped thermal elastic sheets

TL;DR

This study uses molecular dynamics to reveal a tilt phase in thermally fluctuating elastic sheets with one end clamped, showing a spontaneous symmetry-breaking transition influenced by aspect ratio and temperature.

Contribution

It introduces the discovery of a tilt phase in clamped elastic sheets and develops an analytic model predicting phase behavior based on geometry and thermal effects.

Findings

Identification of a tilt phase breaking reflection symmetry

Development of an analytic model matching simulation results

Demonstration of geometric control over mechanical response

Abstract

Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here we use molecular dynamics (MD) to study the vibrations of a thermally fluctuating two-dimensional elastic sheet with one end clamped at its zero-temperature length. We uncover a tilt phase in which the sheet fluctuates about a mean plane inclined with respect to the horizontal, thus breaking reflection symmetry. We determine the phase behavior as a function of the aspect ratio of the sheet and the temperature. We show that tilt may be viewed as a type of transverse buckling instability induced by clamping coupled to thermal fluctuations and develop an analytic model that predicts the tilted and untilted regions of the phase diagram. Qualitative agreement is found with the MD simulations. Unusual response driven by control of purely geometric quantities like the aspect ratio, as opposed to external fields, offers a very rich playground for two-dimensional mechanical metamaterials.