Geometry and physics of wrinkling.
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
Physical Review Letters
|March 14, 2003
Summary
This study presents a general theory for wrinkling in thin elastic sheets, revealing simple scaling laws for wrinkle wavelength and amplitude. These findings could enable a new assay for characterizing thin membrane mechanics.
Area of Science:
- Materials Science
- Solid Mechanics
- Physics of Soft Matter
Background:
- Wrinkling in thin elastic sheets is a common phenomenon observed across various length scales.
- Understanding the mechanics of wrinkling is crucial for applications ranging from cellular substrates to textiles.
Purpose of the Study:
- To develop a general theory for the wrinkling of stretched elastic sheets.
- To derive scaling laws governing wrinkle wavelength and amplitude.
- To explore the potential of wrinkling phenomena for mechanical characterization of thin membranes.
Main Methods:
- Utilizing elementary geometry and the physics of bending and stretching.
- Developing a theoretical framework valid far from the instability onset.
- Deriving scaling relationships based on material properties and geometry.
Main Results:
- Established a general theory for wrinkling in thin elastic sheets.
- Derived scaling laws: wrinkle wavelength (λ) scales as K^(-1/4) and amplitude (A) scales with wavelength (λ).
- Identified K as stiffness from an
- elastic substrate
- effect.
Conclusions:
- The derived scaling laws provide fundamental insights into the physics of elastic sheet wrinkling.
- The proposed theory and scaling laws can form the basis for a quantitative wrinkling assay.
- This assay could offer a highly sensitive method for the mechanical characterization of thin solid membranes.
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