  We study the non-monotonic force-extension behaviour of helical ribbons using
a new model for inextensible elastic strips. Unlike previous rod models our
model predicts hysteresis behaviour for low-pitch ribbons of arbitrary material
properties. Associated with it is a first-order transition between two
different helical states as observed in experiments with cholesterol ribbons.
Numerical solutions show non-uniform uncoiling with hysteresis also occurring
under controlled tension. They furthermore reveal a new uncoiling scenario in
which a ribbon of very low pitch shears under tension and successively releases
a sequence of almost planar loops. Our results may be relevant for nanoscale
devices such as force probes.
