Geometrically driven wrinkling observed in free plastic sheets and leaves
Geometrically driven wrinkling observed in free plastic sheets and leaves
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DOI：
10.1103/physreve.75.046211
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发表时间：
2007-04-01
影响因子：
2.4
通讯作者：
Swinney, Harry L.
中科院分区：
文献类型：
--
作者：
Sharon, Eran;Roman, Benoit;Swinney, Harry L.
我们已经测量了发生在沿着撕裂的塑料片边缘的多尺度扭曲。由撕裂产生的塑性变形在板上定义了一个新的度量，然后弹性松弛。由此产生的皱纹图案对应于不同波长的波的叠加。作为到边缘的距离的函数的图案的变化的测量揭示了一组过渡，其中每一个将新的模式添加到级联。级联中的波长λ取决于由片材边缘附近的度量给出的几何长度尺度L-geo和与t（0.3）L（geo）（0.7）成比例的片材厚度t：λ。这种缩放意味着在极限t -> 0中波长会消失。这种行为的一个可能的几何起源进行了讨论。最后，我们表明，我们的测量和分析技术是适用于一些波浪形图案的树叶的研究。这些测量结果表明，波浪形叶片的内在几何形状类似于撕裂的塑料片。这支持了这样一种可能性，即某些叶子通过自发的扭曲形成波，而不是通过明确的三维结构。
We have measured the multiscale wrinkling that occurs along the edge of torn plastic sheets. The plastic deformations produced by tearing define a new metric on the sheet, which then relaxes elastically. The resultant patterns of wrinkles correspond to a superposition of waves of different wavelengths. Measurements of the variation of the pattern as a function of the distance from the edge reveal a set of transitions, each of which adds a new mode to the cascade. The wavelengths lambda in the cascade depend on both a geometrical length scale L-geo given by the metric near the sheet's edge, and the sheet thickness t: lambda proportional to t(0.3)L(geo)(0.7). This scaling implies vanishingly short wavelengths in the limit t -> 0. A possible geometrical origin of this behavior is discussed. Finally, we show that our measurement and analysis techniques are applicable to the study of some wavy patterns of leaves. These measurements reveal that the intrinsic geometry of a wavy leaf resembles that of the torn plastic sheets. This supports the possibility that some leaves form waves through a spontaneous wrinkling, rather than through an explicit three-dimensional construction.