Crumpling Transition — Elastic Sheet

An elastic sheet (Young modulus Y, bending stiffness κ ~ Yh²) transitions from flat to crumpled via ridge and vertex singularities. Energy concentrates in 1D ridges (E ~ κ^(1/3)(F·L)^(2/3)) and conical vertices. Controlled by the FvK number: Γ = YL²/κ.

Energy: ridges=0 vertices=0 | Phase: flat