弹性带中几何挫折的层次性：从一般渐近理论得到的形状转变和能量标度
Hierarchy of Geometrical Frustration in Elastic Ribbons: shape-transitions and energy scaling obtained from a general asymptotic theory
摘要：
在许多情况下，几何阻挫弹性带根据它们的宽度和厚度之间的关系表现出显著的构型变化。我们表明，这样的过渡的存在，以及它发生的缩放，强烈依赖于系统考虑。使用渐近的方法，处理的宽度作为一个小参数，我们发现导致的挫折和预测的存在和缩放的形状转变的能量项。我们详细研究了5种不同类型的沮丧丝带与不同的形态依赖于丝带的宽度：一个尖锐的形状过渡在临界宽度，一个温和的过渡与中间制度，并没有过渡。我们表明，我们的方法的预测与两种不同实验系统的实验结果相匹配：预应力橡胶双层和4D打印热塑性塑料，在各种几何设置中。
英文摘要：
Geometrically frustrated elastic ribbons exhibit, in many cases, significant changes in configuration depending on the relation between their width and thickness. We show that the existence of such a transition, and the scaling at which it occurs, strongly depend on the system considered. Using an asymptotic approach, treating the width as a small parameter, we find the leading energy terms resulting from the frustration and predict the existence and scaling of the shape transition. We study in detail 5 different types of frustrated ribbons with a different morphological dependence on ribbon's width: a sharp shape-transition at a critical width, a moderate transition with an intermediate regime, and no transition at all. We show that the predictions of our approach match experimental results from two different experimental systems: prestressed rubber bilayers and 4D printed thermoplastics, in a wide variety of geometric settings.
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