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

We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle $2 α$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness $σ$ and the bending angle. We show that the minimum energy scales as $σ^{5/3} α^{7/3}$. 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 $σ$.

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