Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower. Anticipating and controlling these morphologies is crucial to a variety of applications involving textiles, synthetic skins, and inflatable structures. Here we show that a "wrinkle-to-crumple" transition, previously observed in specific settings, is a ubiquitous response for confined sheets. This unified picture is borne out of a suite of model experiments on polymer films confined to liquid interfaces with spherical, hyperbolic, and cylindrical geometries, which are complemented by experiments on macroscopic membranes inflated with gas. We use measurements across this wide range of geometries, boundary conditions, and lengthscales to quantify several robust morphological features of the crumpled phase, and we build an empirical phase diagram for crumple formation that disentangles the competing effects of curvature and compression. Our results suggest that crumples are a generic microstructure that emerge at large curvatures due to a competition of elastic and substrate energies.

中文翻译：

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压皱是密闭薄板中应力集中的一般不稳定性

薄的弹性固体很容易变形为无数个三维形状，这些形状可能像在皱巴巴的糖果包装纸中那样包含尖锐的局部结构，也可能具有平滑且分散的特征，如花朵的起伏边缘。预测和控制这些形态对于涉及纺织品，人造皮肤和充气结构的各种应用至关重要。在这里，我们显示了以前在特定设置中观察到的“起皱到皱折”过渡，这是对受限板的普遍响应。这张统一的图片来自一组聚合物薄膜的模型实验，该聚合物薄膜被限制在具有球形，双曲线和圆柱几何形状的液体界面上，并辅之以用气体充气的宏观膜的实验。我们在各种几何形状中使用测量值，边界条件和长度标度来量化皱折相的几个稳健的形态特征，我们建立了压皱形成的经验相图，以解开曲率和压缩的竞争效应。我们的结果表明，皱纹是一种通用的微观结构，由于弹性和底物能量的竞争而出现在大曲率处。