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Forced crumpling of self-avoiding elastic sheets

Nature Materials volume 5, pages 216–221 (2006)Cite this article

Abstract

Thin elastic sheets are important materials across length scales ranging from mesoscopic (polymerized membranes, clay platelets, virus capsids) to macroscopic (paper, metal foils). The crumpling of such sheets by external forces is characterized by the formation of a complex pattern of folds. We have investigated the role of self-avoidance, the fact that the sheets cannot self-intersect, for the crumpling process by large-scale computer simulations. At moderate compression, the force–compression relations of crumpled sheets for both self-avoiding and phantom sheets are found to obey universal power-law behaviours. However, self-avoiding sheets are much stiffer than phantom sheets and, for a given compression, develop many more folds. Moreover, self-avoidance is relevant already at very small volume fractions. The fold-length distribution for crumpled sheets is determined, and is found to be well-described by a log-normal distribution. The stiffening owing to self-avoidance is reflected in the changing nature of the sheet-to-sheet contacts from line-like to two-dimensionally extended with increasing compression.

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Figure 1: Schematic representation of the computer experiments.
Figure 2: Three-dimensional shape of a cone and a crumpled sheet.
Figure 3: Radius and energy as a function of the external force.
Figure 4: Fold patterns and energy distributions of crumpled sheets.
Figure 5: Contacts between different parts of a crumpled self-avoiding sheet.
Figure 6: Uniaxial and radial compression of sheets in cylindrical confinement.

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Acknowledgements

The authors thank N. Kirchgeßner for help in developing the image-analysis procedure and D. M. Kroll and D. R. Nelson for valuable discussions.

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  1. Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425, Jülich, Germany

    G. A. Vliegenthart & G. Gompper

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  1. G. A. Vliegenthart
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  2. G. Gompper
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Correspondence to G. A. Vliegenthart or G. Gompper.

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Vliegenthart, G., Gompper, G. Forced crumpling of self-avoiding elastic sheets. Nature Mater 5, 216–221 (2006). https://doi.org/10.1038/nmat1581

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