Conditions for crumpling: thin elastic manifold
Metric: preferred distance
between all pairs of points
Elasticity: energy cost for
altering this distance.
Thin manifold: d-dimensional set of points much
smaller in one direction than the others
Energy =
Bending B
Stretching S
1
g
R
R
Energy cost simplifies when
local deformation is smooth
curvature
strain
Smooth: g << 1; R >> h
h