  We investigate experimentally and model the mechanical response of a soft
Hookean ribbon submitted to large twist $\eta$ and longitudinal tension $T$,
under clamped boundary conditions. We derive a formula for the torque $M$ using
the \FvK equations up to third order in twist, incorporating a twist-tension
coupling. In the stable helicoid regime, quantitative agreement with
experimental data is obtained. When twisted above a critical twist $\eta_L(T)$,
ribbons develop wrinkles and folds which modify qualitatively the mechanical
behavior. We show a surprisingly large longitudinal contraction upon twist,
reminiscent of a Poynting effect, and a much lower torsional stiffness. Far
from threshold, we identify two regimes depending on the applied $T$. In a
high-$T$ regime, we find that the torque scales as $\eta\cdot T$ and the
contraction as $\eta^2$, in agreement with a far from threshold analysis where
compression and bending stresses are neglected. In a low-$T$ regime, the
contraction still scales as $\eta^2$ but the torque appears $T$-independent and
linear with $\eta$. We argue that the large curvature of the folds now
contribute significantly to the torque. This regime is discussed in the context
of asymptotic isometry for very thin plates submitted to vanishing tension but
large change of shape, as in crumpling.
