Thermal buckling and symmetry breaking in thin ribbons under compression

TL;DR

This paper develops a theoretical framework incorporating thermal fluctuations to predict buckling behavior in thin ribbons under compression, validated by molecular dynamics simulations, extending beyond classical thin-plate theory at higher temperatures.

Contribution

It introduces a unifying theoretical approach that accounts for thermal effects on buckling in ribbons, bridging the gap between low-temperature thin-plate theory and thermalized conditions.

Findings

Renormalized elastic constants depend on ribbon width and thermal length.

Buckling behavior can be mapped to a mean-field model for short ribbons.

Simulations confirm the theoretical predictions across temperature regimes.

Abstract

Understanding thin sheets, ranging from the macro to the nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due to in-plane compression can be a key feature in designing new materials. While thin-plate theory can predict critical buckling thresholds for thin frames and nanoribbons at very low temperatures, a unifying framework to describe the effects of thermal fluctuations on buckling at more elevated temperatures presents subtle difficulties. We develop and test a theoretical approach that includes both an in-plane compression and an out-of-plane perturbing field to describe the mechanics of thermalised ribbons above and below the buckling transition. We show that, once the elastic constants are renormalised to take into account the ribbon's width (in units of the thermal length scale), we can map the physics onto a mean-field treatment of buckling, provided the length is short compared to a ribbon persistence length. Our theoretical predictions are checked by extensive molecular dynamics simulations of thin thermalised ribbons under axial compression.