Effects of supporting-frame flexibility on the sequential snap-through and recoverability of curved beam mechanical metamaterials

This study investigates the effects of supporting-frame flexibility on the sequential snap-through and recoverability of curved beam mechanical metamaterials, with a focus on the state-dependent interaction. A theoretical model is developed to capture the snap-through instability of a curved beam interacting with a flexible supporting frame. The analysis reveals that reducing the stiffness of the horizontal or vertical beams shifts the buckling behavior from bistable to monostable, reshaping the regime boundaries and widening the range of geometric parameters that yield a recoverable state. Subsequently, a piecewise model is established to describe the sequential snap-through process and the state-dependent interaction. This model captures the transition of the horizontal beam from axial deformation to combined axial and bending deformation as horizontal forces redistribute, revealing the competition between different buckling mechanisms. Leveraging these insights, a recoverable damping mechanical metamaterial with a flexible supporting frame is proposed. The results reveal a design trade-off between structural strength, stiffness, equivalent damping ratio, and recoverability, providing a basis for the inverse design of mechanical metamaterials. Finite element simulations validate the theoretical findings. This work aims to offer design insights into mechanical metamaterials with potential for seismic applications.