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Stretching an Elastic Loop: Crease, Helicoid, and Pop Out
Yasuaki Morigaki1, Hirofumi Wada2, Yoshimi Tanaka1
1Graduate School of Environmental and Information Sciences, Yokohama National University, Yokohama 240-8501, Japan.
Physical Review Letters
|November 19, 2016
Summary
Thin ribbons exhibit surprising shape changes when stretched. Researchers identified three transition types (crease, helicoid, pop out) and found the pop-out transition depends on ribbon width and thickness.
Area of Science:
- Physics
- Materials Science
- Mechanical Engineering
Background:
- Thin structures under geometric constraints can display complex behaviors.
- Paper strips provide a simple model for studying these phenomena.
Purpose of the Study:
- To investigate the shape transitions of a stretched, looped ribbon.
- To classify these transitions based on ribbon geometry.
- To understand the underlying physical mechanisms governing these shape changes.
Main Methods:
- Experimental observation of shape transitions in stretched ribbons.
- Theoretical analysis using Kirchhoff rod theory.
- Numerical simulations and scaling arguments.
Main Results:
- Identified three distinct shape transition types: crease, helicoid, and pop out.
- Developed a transition-type diagram based on experimental data.
- Established a characteristic length scale (ξ∼b²/h) governing the pop-out transition, where b is width and h is thickness.
- Highlighted the influence of bending elasticity anisotropy and plastic deformation on shape selection.
Conclusions:
- The study provides a comprehensive understanding of shape transitions in constrained ribbons.
- Geometric parameters and material properties critically influence the observed shape transformations.
- The findings have implications for the design and behavior of thin, flexible structures.
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