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Published on: January 5, 2019
Intrinsically anomalous roughness of randomly crumpled thin sheets
Alexander S Balankin1, Orlando Susarrey Huerta, Rolando Cortes Montes de Oca
1Grupo "Mecánica Fractal," Instituto Politécnico Nacional, México D.F., 07738 Mexico.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
Folding ridges influence paper crumpling scaling properties. Ridge length scaling determines the mass fractal dimension, revealing self-affine invariance or anomalous roughness based on deformation competition.
Area of Science:
- Physics
- Materials Science
- Surface Science
Background:
- Randomly crumpled sheets exhibit complex scaling properties.
- Folding ridges are a key feature in the mechanical behavior of thin sheets.
- Understanding these properties is crucial for material science applications.
Purpose of the Study:
- To investigate the impact of folding ridges on the scaling properties of crumpled paper sheets.
- To determine how bending and stretching deformations influence ridge length scaling.
- To analyze the resulting fractal dimensions and surface roughness characteristics.
Main Methods:
- Experimental study of randomly crumpled paper sheets in folded and unfolded states.
- Analysis of mean ridge length scaling with sheet size.
- Calculation of mass fractal dimension and surface self-affine invariance exponents.
Main Results:
- Mean ridge length scales with sheet size, governed by a scaling exponent (μ) reflecting bending-stretching deformation competition.
- The mass fractal dimension of crumpled balls is found to be D{M}=2/μ.
- Surfaces exhibit self-affine invariance or anomalous roughness depending on whether μ is less than or greater than the phantom membrane size exponent (ν{ph}).
Conclusions:
- Folding ridges play a critical role in defining the scaling behavior of crumpled paper.
- The study provides insights into the relationship between material properties, deformation, and the resulting fractal geometry.
- Findings contribute to understanding the physics of crumpled materials and their surface characteristics.
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