Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite. Using both theoretical and computational techniques, we characterize the bifurcations of such a mechanical system, in which the axial force and the natural curvature of the beam are used as control parameters. We show that, in the presence of a straight support, the rod can deform into shapes exhibiting helices and perversions, namely transition zones connecting together two helices with opposite chirality. The mathematical predictions of the proposed model are also compared with some experiments, showing a good quantitative agreement. In particular, we find that the buckled configurations may exhibit multiple perversions and we propose a possible explanation for this phenomenon based on the energy landscape of the mechanical system.

可以利用机械不稳定性来设计创新的结构，该结构能够在存在外部刺激的情况下改变其形状。在这项工作中，我们导出了一个弹性梁的数学模型，该弹性梁受到轴向力并被约束沿刚性支撑平稳滑动，其中杆中线和约束之间的距离是固定且有限的。使用理论和计算技术，我们都对这种机械系统的分叉进行了表征，其中将梁的轴向力和自然曲率用作控制参数。我们表明，在有直支撑的情况下，杆可变形为呈现出螺旋和变态的形状，即将两个具有相反手性的螺旋连接在一起的过渡区域。该模型的数学预测结果也与一些实验进行了比较，显示出良好的定量一致性。特别是，我们发现弯曲的构型可能表现出多个变态，并且我们基于机械系统的能量格局提出了对此现象的可能解释。