Department of Physics, Syracuse University, Syracuse, NY 13244.
BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244.
Proc Natl Acad Sci U S A. 2023 Mar 14;120(11):e2216786120. doi: 10.1073/pnas.2216786120. Epub 2023 Mar 10.
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. A geometric model, which considers the sheet as inextensible yet free to compress, has been shown to capture the gross shape of the sheet. However, the precise meaning of such predictions, and how the gross shape constrains the fine features, remains unclear. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its side profiles and horizontal cross-sections, we discover that the mean behavior of the film is the physical observable that is predicted by the geometric model, even when the buckled structures atop it are large. We then propose a minimal model for the horizontal cross-sections of the balloon, as independent elastic filaments subjected to an effective pinning potential around the mean shape. Despite the simplicity of our model, it reproduces a broad range of phenomena seen in the experiments, from how the morphology changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.
虽然薄膜通常以平面片或卷材的形式制造，但它们经常被强制形成三维（3D）形状，从而在多个长度尺度上产生大量结构。为了理解这种复杂的响应，以前的研究要么集中在整体宏观形状上，要么集中在装饰它的小尺度屈曲上。一个考虑到薄片不可延展但可以自由压缩的几何模型已被证明可以捕捉薄片的宏观形状。然而，这些预测的确切含义以及宏观形状如何限制精细特征仍然不清楚。在这里，我们研究了一个薄膜气球作为一个原型系统，它涉及具有大振幅波动的双曲度宏观形状。通过探测其侧轮廓和水平横截面，我们发现即使顶部的屈曲结构很大，薄膜的平均行为也是由几何模型预测的物理可观测量。然后，我们为气球的水平横截面提出了一个最小模型，将其作为独立的弹性细丝，在平均形状周围受到有效钉扎势的作用。尽管我们的模型很简单，但它再现了实验中看到的广泛现象，从形态随压力的变化到皱纹和褶皱的详细形状。我们的结果建立了一种在封闭表面上一致地结合全局和局部特征的方法，这可以帮助设计可膨胀结构，或为生物模式提供见解。
