Metamaterials with in situ tunable bending properties

Mechanical metamaterials with tunable bending stiffness are significant for realizing smart adaptable machines or structures composed of beams, shells and plates. However, different from tuning longitudinal stiffness, realizing broad-range, continuous, and in situ (without global shape morphing) tunability of bending properties remains a major challenge. Here, we report a deformation conversion principle for designing meta-beams/plates that offer such extraordinary tunability. The metamaterials incorporate planetary gear assemblies as tension-compression fibers within sandwich beams or plates, effectively transferring the localized tunable longitudinal stiffness of these geared units into the global tunable bending stiffness. This principle enables diverse tunable bending modes, including the static bending deformation, vibrational modal shapes and frequencies, and bending wave bandgaps. Their smoothly tunable properties and mechanisms are demonstrated based on analytical, numerical and experimental methods. This work offers a new pathway for developing structures with adaptively tunable bending properties that are free from the constraints of intrinsic material properties, elucidating innovations and applications of mechanical metamaterials and structures for intelligent systems.