Recent experiments have reported an intriguing phenomenon of self-sustained rolling of a polymer rod on a flat and hot surface (Baumann et al., 2018; Ahn et al., 2018; Bazir et al., 2020). Although it has been postulated that the rod rolling is driven by its inhomogeneous thermal expansion, a quantitative thermo-mechanics model of the phenomenon, capable of explaining all the experimental observations, is not yet available. In this article, we have constructed a thermo-mechanics model of a rod rolling on a hot surface. In the model, we calculate the thermally induced deformation and stress field in the rod during its steady rolling, further enabling the prediction of its rolling speed at different conditions. Our model has also successfully predicted bistable state of the rod, which agrees well with the experimental observations.

最近的实验报告了一种有趣的现象，即聚合物棒在平坦和热的表面上自持滚动（Baumann等人，2018; Ahn等人，2018; Bazir等人，2020）。尽管已经假定棒材的轧制是由其不均匀的热膨胀驱动的，但尚无能够解释所有实验观察结果的定量热力学模型。在本文中，我们构建了在热表面上滚动的棒的热力学模型。在模型中，我们计算了棒材在稳定轧制过程中的热变形和应力场，从而进一步预测了不同条件下的轧制速度。我们的模型还成功地预测了棒的双稳态，这与实验观察非常吻合。