Crumpling singularities in real sheets
ridge
d-cone
X
h
Width w adopts new length scale controlled by stretching
ridge
d-cone vertex
crescent singularity at tip controlled by stretching
w ~ X (X/h)-1/3
–Chicago group 1995  http://jfi.uchicago.edu/~tten/Crumpling/
–Cerda, Chaieb, Melo, Mahadevan 1998
h <<  w  << X
w
energy ~ log X/h