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Geometrically driven wrinkling observed in free plastic sheets and leaves
Eran Sharon1, Benoît Roman, Harry L Swinney
1The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Summary
Researchers studied wrinkling patterns on torn plastic sheets, revealing a cascade of wave modes. This phenomenon, governed by sheet thickness and edge geometry, may explain natural leaf waviness through spontaneous wrinkling.
Area of Science:
- Physics
- Materials Science
- Biology
Background:
- Wrinkling is a common phenomenon in thin sheets.
- The formation of multiscale wrinkles is not fully understood.
Purpose of the Study:
- To investigate the multiscale wrinkling patterns on torn plastic sheets.
- To establish a quantitative relationship between wrinkle characteristics and material/geometric properties.
- To explore the applicability of these findings to natural biological structures like leaves.
Main Methods:
- Experimental measurement of wrinkle patterns on torn plastic sheets.
- Analysis of plastic deformation and elastic relaxation.
- Development of a scaling law for wrinkle wavelengths.
- Comparison of wrinkling patterns with leaf morphology.
Main Results:
- Wrinkling patterns result from a superposition of waves with varying wavelengths.
- A scaling law was derived: lambda proportional t^0.3 * Lgeo^0.7, where lambda is wavelength, t is thickness, and Lgeo is geometrical length scale.
- The study demonstrated the applicability of the measurement techniques to wavy leaf patterns.
- Leaf intrinsic geometry shows resemblance to torn plastic sheets, suggesting spontaneous wrinkling.
Conclusions:
- Tearing induces plastic deformations that lead to elastic relaxation and multiscale wrinkling.
- The derived scaling law provides a quantitative model for wrinkle formation.
- Spontaneous wrinkling is a plausible mechanism for the formation of wavy patterns in some leaves.
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