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