Unstretchable
d-cone: sets stage for d-cone puzzles
E. Cerda and L.
Mahadavan 1990s
S. Venkataramani
F
s labels point on unit
circle
curves only
perpendicular to radial lines, curvature c(s)
s
Bending energy: B = k ˜_r
dr / r2 ˜
ds c(s)2
rmin
rmax
detached region:
minimizing B ~ finding the shape of a compressed thin rod (Euler).
rim constraints
determine length and compressive force.
Results:
s reaches the rim at sc = 69.9 degrees for small deflection
rim
the force from the rim
is independent of s, except...
an extra impulsive
force acts at the takeoff point: 0.411 F for small deflection
(similar universal
geometry happens in confined fibers.)
log rmax /rmin