Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets
Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets
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DOI：
10.1073/pnas.1521520113
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发表时间：
2016-02-02
影响因子：
11.1
通讯作者：
Davidovitch, Benny
中科院分区：
文献类型：
--
作者：
Paulsen, Joseph D.;Hohlfeld, Evan;Davidovitch, Benny
压缩薄片上的皱纹在自然界和科技中随处可见，从我们额头上的皱纹到皱巴巴的植物叶子，从塑料包装物品上的涟漪到牛奶上的蛋白质膜。目前对皱纹的基本描述符--它们的波长--的理解仅限于平行的、空间上均匀的、几乎是平面的变形。然而，大多数自然产生的皱纹并不符合这些规定。在这里，我们提出了一个方案，定量地解释了超出这种理想化情况的皱纹波长。我们提出了一种综合了机械效应和几何效应的局域定律来控制皱纹波长的空间变化。我们在聚合物薄膜上的实验为其有效性提供了强有力的证据。了解波长如何依赖于薄板和底层液体或弹性亚相的性质，对于使用褶皱来塑造表面形貌、测量薄板的性能或推断施加在薄膜上的力的应用至关重要。
Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles-their wavelength-is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.