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The effect of plasticity in crumpling of thin sheets

Abstract

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges1,2. Scaling properties of a single elastic vertex3,4,5 or ridge have been analysed theoretically6,7,8, and crumpling of a sheet by numerical simulations1,9,10. Real materials are however elasto-plastic11,12,13,14,15 and large local strains induce irreversible plastic deformations. Hence, a numerical model that can be purely elastic or elasto-plastic is introduced. In crumpled elastic sheets, the ridge patterns are found to be similar, independent of the width to thickness (L/h) ratio of the sheet, and the fractal dimension of crumpled sheets is given by scaling properties of the energy and average length of ridges. In crumpled elasto-plastic sheets, such a similarity does not appear as the L/h ratio affects the deformations, and the fractal dimension (Dpl) is thereby reduced. Evidence is also found of Dpl not being universal but dependent on the plastic yield point of the material.

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Figure 1: Crumpling thin sheets inside a spherical shell.
Figure 2: Intersections of crumpled sheets.
Figure 3: Development of facet size and deformation energy during crumpling.
Figure 4: Mean curvature fields and facet size distributions of crumpled sheets.
Figure 5: Relation of sheet width to the final radius of the crumpled configuration.

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Acknowledgements

We are grateful to A. Resnick, M. Kardar, M. Karttunen, R. Metzler and M. den Nijs for very useful discussions. We acknowledge CSC—the Finnish IT Centre for Science for the computing time grant jyy2517.

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Software development: T.T., J.A. Simulations: T.T. Analysis and interpretation: T.T., J.A., J.T. Text: T.T., J.A., J.T.

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Correspondence to T. Tallinen.

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Tallinen, T., Åström, J. & Timonen, J. The effect of plasticity in crumpling of thin sheets. Nature Mater 8, 25–29 (2009). https://doi.org/10.1038/nmat2343

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