  Designing materials or structures that can achieve asymmetric shape-shifting
in response to symmetrically switching stimuli is a promising approach to
enhance the locomotion performance of soft actuators/robots. Inspired by the
geometry of slender leaves of many plants, we find that the thin-walled beam
with a U-shaped cross section exhibits asymmetric deformation behaviors under
bending with opposite orientations. Although this novel mechanical property has
been long noticed and utilized in some applications, its mechanism is still
unclear so far. In this study, we attribute this asymmetric bending behavior of
thin-walled U-shaped beams to the buckling of sidewalls caused by the
bending-induced compressive effect. Based on the Euler-Bernoulli beam theory
and Kirchhoff-Love thin plate theory, a simple but efficient model is
established to derive the critical moment for the sidewall buckling in a
semi-analytical form. Finite element analysis simulations and experiments are
employed to validate the theoretical foundations of our findings. The results
of our work not only shed light on the mechanics underlying the asymmetric
bending behavior of thin-walled U-shaped beams, but also open up new avenues
for the structure design of high-performance soft actuators/robots and other
novel devices.
