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Unfolding of crumpled thin sheets.

F C B Leal¹, M A F Gomes¹

¹Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.

Physical Review. E

|September 16, 2022

Summary

Stretching crumpled sheets reveals their fractal nature. Their stress-strain behavior shifts from linear to a sublinear scaling, indicating hierarchical ridge structures guide the unfolding process.

Area of Science:

Physics
Materials Science
Fractal Geometry

Background:

Crumpled thin sheets exhibit complex fractal structures.
Physical properties are influenced by hierarchical ridge formations.

Purpose of the Study:

Investigate the stress-strain relationship during the stretching of crumpled surfaces.
Analyze stress fluctuations and force peak distributions.
Identify the scaling behavior and its relation to fractal properties.

Main Methods:

Experimental measurement of stress-strain relations.
Analysis of stress fluctuations and force peak statistics.
Characterization of fractal properties using scaling exponents.

Main Results:

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Observed a transition in pull stress from a linear Hookean regime to sublinear scaling.
Determined a scaling exponent of 0.65±0.03, identified as the Hurst exponent.
Demonstrated that the unpacking of crumpled sheets follows a hierarchical order of ridges.

Conclusions:

The stretching of crumpled sheets exhibits distinct phases governed by their fractal geometry.
The Hurst exponent characterizes the mechanical response, linking macroscopic behavior to microscopic structure.
Hierarchical ridge organization plays a crucial role in the unfolding dynamics of crumpled materials.