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Fold analysis of crumpled sheets using microcomputed tomography.

Yumino Hayase¹, Hitoshi Aonuma², Satoshi Takahara³

¹Department of Physics, Kyushu University, Fukuoka 819-0395, Japan.

Physical Review. E

|September 16, 2021

Summary

This summary is machine-generated.

Crumpled paper balls exhibit self-similar structures, confirmed using micro-computed tomography (micro-CT). This structural similarity across different sizes suggests universal scaling properties in crumpled materials like paper, cellophane, and foil.

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Area of Science:

Materials Science
Physics
Complex Systems

Background:

Hand-crumpled paper balls possess intricate structures with creases and vertices.
These structures exhibit simple scaling properties, hinting at underlying self-similarity.
Understanding the 3D internal structure of crumpled materials is challenging without unfolding.

Purpose of the Study:

To investigate the internal structure of crumpled paper balls using micro-computed tomography (micro-CT).
To quantify the fractal dimensions and scaling properties of crumpled materials.
To explore the self-similarity and structural randomness of lines on crumpled surfaces.

Main Methods:

Utilized micro-computed tomography (micro-CT) to reconstruct the 3D internal structure of crumpled paper, cellophane, and aluminum foil.
Applied power law analysis to relate mass and radius of gyration to determine mass fractal dimension (D_M).
Employed box counting method in real space and structure factors in Fourier space to determine fractal dimension (d_f).
Analyzed the Hurst exponent (H) of lines drawn on crumpled surfaces to assess structural randomness.

Main Results:

Obtained a mass fractal dimension (D_M) of 2.7±0.1 for crumpled paper balls.
Determined fractal dimensions (d_f) for the internal structure of crumpled paper, cellophane, and aluminum foil to be between 2.5 and 2.8.
Found consistency between D_M and d_f, supporting self-similarity across different crumpled material sizes.
Characterized line structures on crumpled paper with Hurst exponents of approximately 0.9 (short scale) and 0.5 (long scale).

Conclusions:

The self-similarity observed in individual crumpled balls contributes to size-independent scaling properties.
Micro-CT is an effective non-destructive method for analyzing the 3D structure of crumpled materials.
Crumpled paper, cellophane, and foil share similar fractal characteristics, suggesting universal behavior in crumpled systems.