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Entropic rigidity of a crumpling network in a randomly folded thin sheet
Alexander S Balankin1, Orlando Susarrey Huerta
1Fractal Mechanics Group, National Polytechnic Institute, Avanzados del Instituto Politécnico Nacional, México D.F., Mexico 07738.
Summary
We studied randomly folded sheets under compression, finding their mechanical response depends on crumpling network entropy. An explicit force-compression relationship was derived, matching experimental data for folded matter.
Area of Science:
- Materials Science
- Physics
- Statistical Mechanics
Background:
- Randomly folded sheets exhibit complex mechanical behaviors.
- Understanding crumpling networks is crucial for predicting material properties.
Purpose of the Study:
- To investigate the mechanical response of randomly folded hyperelastic and elastoplastic sheets under uniaxial compression.
- To analyze the statistical properties of crumpling networks.
- To establish a force-compression relationship for folded matter.
Main Methods:
- Experimental study of sheet response to uniaxial compression.
- Theoretical analysis of crumpling network entropy.
- Derivation of a force-compression relationship based on Edwards's ideas for granular materials.
Main Results:
- Mechanical behavior is governed by the shape dependence of crumpling network entropy.
- An explicit force-compression relationship accurately fits experimental data.
- Entropic rigidity modulus scales with mass density with a universal exponent.
Conclusions:
- The study provides a quantitative model for the mechanical response of randomly folded materials.
- Findings highlight the importance of network entropy in material mechanics.
- The derived scaling law offers insights into the universal properties of crumpled matter.
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