Sharon Eran, Roman Benoît, Swinney Harry L
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):046211. doi: 10.1103/PhysRevE.75.046211. Epub 2007 Apr 24.
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 Lgeo given by the metric near the sheet's edge, and the sheet thickness t: lambda proportional t0.3Lgeo0.7. 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.
我们测量了沿撕裂塑料片边缘出现的多尺度皱纹。撕裂产生的塑性变形在片材上定义了一种新的度量，然后该片材会弹性松弛。由此产生的皱纹图案对应于不同波长波的叠加。对图案随距边缘距离变化的测量揭示了一组转变，其中每一个转变都会为级联增加一种新模式。级联中的波长λ既取决于由片材边缘附近的度量给出的几何长度尺度Lgeo，也取决于片材厚度t：λ与t^0.3Lgeo^0.7成正比。这种标度意味着在t→0的极限情况下波长会短到趋近于零。我们讨论了这种行为可能的几何起源。最后，我们表明我们的测量和分析技术适用于研究一些叶片的波浪状图案。这些测量结果表明，波浪状叶片的内在几何形状与撕裂的塑料片相似。这支持了一些叶片通过自发起皱而不是通过明确的三维构造形成波浪的可能性。
