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

Extreme Contractility and Torsional Compliance of Soft Ribbons under High Twist