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Metabeams with programmable nonlinear bending response
Recent advances in mesoscale material architecture have enabled the design of structures exhibiting nonclassical mechanical responses, including auxetic behavior, mode coupling (e.g., stretching–bending and stretching–twisting), and exceptional stiffness-to-weight ratios. Inspired by the nonlinear bending response of a carpenter’s measuring tape and the pronounced drooping of U-shaped plant petioles under water stress, we investigate the bending behavior of rectangular beams decorated with one or more longitudinal vertical fins.
During bending, longitudinal stretching of the fins couples to the beam curvature, inducing transverse compression within the fins. Beyond a critical curvature, this compression triggers fin buckling, which we rationalize in terms of the governing geometric parameters. Fin buckling leads to an abrupt reduction of the beam’s effective moment of inertia, giving rise to a non-monotonic moment–curvature relationship closely analogous to that observed in carpenter’s tapes.
By incorporating pillars that engage only beyond a prescribed curvature, we introduce curvature-dependent mechanical hardening. When combined with the fins, this strategy enables the programming of rich, highly tunable, and non-monotonic torque–curvature responses. An inverse design framework is developed to achieve on-demand torque profiles and is validated experimentally.
Exploiting this complex torque response, we further show that embedding fin-decorated beams into pneumatic bending actuators induces a snap-through instability, resulting in rapid actuation and a hysteretic mechanical response. This behavior enables fast, programmable motion.