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.

在许多情况下，几何受挫的弹性带会根据其宽度和厚度之间的关系显示出显着的结构变化。我们表明，这种转变的存在及其发生的规模在很大程度上取决于所考虑的系统。使用渐近方法，将宽度视为一个小参数，我们找到了由挫折产生的主要能量项，并预测了形状转换的存在和缩放。我们详细研究了 5 种不同类型的受挫带，它们对带的宽度具有不同的形态依赖性：临界宽度处的急剧形状过渡，中间状态的适度过渡，以及根本没有过渡。我们表明我们的方法的预测与来自两个不同实验系统的实验结果相匹配：