Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge

Abstract

We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle $2\alpha$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness $\sigma$ and the bending angle. We show that the minimum energy scales as ${\sigma }^{5/3}{\alpha }^{7/3}$. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as $\sigma$.

15 pages, 2 figures, iopart style files; Changes - 10/25 -- Changes to the introduction, fixed the references

References in corpus (1)

• Singularities, Structures and Scaling in Deformed Elastic m-Sheets

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