论文标题

强烈弯曲的床单中的总体和精细结构的相互作用

Interplay of gross and fine structures in strongly-curved sheets

论文作者

He, Mengfei, Démery, Vincent, Paulsen, Joseph D.

论文摘要

尽管薄膜通常是在平面或卷中制造的,但通常被迫分为三维形状,在多个长度尺度上产生了大量的结构。现有的理论方法通过将不同尺度的行为分开并将其范围限制为一个,从而取得了进步。在大量限制下,已经提出了一个几何模型来预测纸张的总形状,该纸张平均表现出精细的特征。但是,总体形状的实际含义及其如何限制精美特征,尚不清楚。在这里,我们研究了一个薄膜的气球作为一种典型系统,涉及双重弯曲的总形状,并具有较大的振幅起伏。通过探测其剖面和横截面,我们发现几何模型捕获了膜的平均行为。然后,我们提出了一个小气球横截面的最小模型,因为独立的弹性丝在平均形状周围具有有效的固定电势。这种方法使我们能够始终如一地结合全球和本地功能。尽管我们的模型很简单,但它在实验中重现了广泛的现象,从形态如何随压力变化到皱纹和褶皱的详细形状。我们的结果建立了一条新的途径,以了解封闭的表面上有限的扣结构,这可以帮助设计充气结构,或者提供对生物学模式的见解。

Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional shapes, producing a plethora of structures across multiple length-scales. Existing theoretical approaches have made progress by separating the behaviors at different scales and limiting their scope to one. Under large confinement, a geometric model has been proposed to predict the gross shape of the sheet, which averages out the fine features. However, the actual meaning of the gross shape, and how it 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 profiles and cross sections, we discover that the geometric model captures the mean behavior of the film. We then propose a minimal model for the balloon cross sections, as independent elastic filaments subjected to an effective pinning potential around the mean shape. This approach allows us to combine the global and local features consistently. 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 new route to understanding finite buckled structures over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.

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