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.

了解从宏观到纳米尺度的薄板，可以控制机械性能，例如可变形性。由于平面内压缩而导致的平面外屈曲可能是设计新材料的关键特征。尽管薄板理论可以预测非常低的温度下薄框架和纳米带的临界屈曲阈值，但描述更高温度下热波动对屈曲的影响的统一框架存在着细微的困难。我们开发并测试了一种理论方法，该方法包括平面内压缩和平面外扰动场，以描述屈曲过渡上方和下方的热化碳带的力学原理。我们表明，一旦弹性常数被重新归一化以考虑色带的宽度（以热长度标尺为单位），我们可以将物理学映射到屈曲的平均场处理上，前提是该长度比色带持久性长度短。我们的理论预测通过轴向压缩下薄热带的广泛分子动力学模拟进行了检验。