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