The energy of crumpled sheets in Foppl-von Karman plate theory

We study investigate a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$, using the Foppl--von Karman ansatz in a geometrically linear setting. We study the associated variational problem, and show the existence of a minimizer for the elastic energy. We also prove rigorous upper and lower bounds for the minimum energy of this configuration in terms of the plate thickness and the bending angle, and we also obtain results for the structure of the elastic ridge along it's length.