Metastructures composed of snapping beams are capable of deforming into a series of stable states, enabling them to realize shape reconfigurations. In this paper, we present the design of a metastructure-based morphing surface that is able to exhibit a series of stable configurations with different curvatures. Using theoretical, numerical, and experimental approaches, we study the snap-through transition between the initially flat and the curved stable configurations. Effects of geometric parameters on the snap-through and curvatures are systematically investigated. Results show that the beam thickness is important for tuning the snap-through response, while the curvature can be tuned by changing the beam height and the horizontal span of the structures. Furthermore, an analytical model is developed to investigate the structural nonlinear deformations. It is shown that the proposed model can predict the snap-through transition properly. The structural stability can be controlled by setting proper values for t/L and h/L (t, h, and L represents the beam thickness, height and span, respectively). Finally, it is demonstrated that based on two-dimensional arrangements of bi-stable elements, various stable configurations, like corrugations in different directions, can be imposed to the surface.

Multi-stable metastructures composed of curved beams can switch to a series of stable configurations via elastic snap-through transitions. The elastic deformations allow metastructures to function as reusable energy absorbers. However, conventional metastructure designs based on solid beams often result in relatively low energy dissipation. In this work, it is found that by increasing the beam unit's bending stiffness while keeping the volume/mass constant, energy dissipation of the metastructure can be largely improved. Based on this observation, we propose two types of structural designs (lattice and hollow cross-section design) as building blocks for multi-stable metastructures. The lattice design is realized by incorporating lattice structures into pre-shaped beams while for the hollow cross-section design, a box-shaped cross section is adopted. The proposed structures are experimentally characterized under cyclic loading and are shown to exhibit sequential snap-through transitions with relatively large energy dissipation. Results show the snap-through behavior can be further tailored through tuning structural in-plane thickness. Effects of geometric parameters on snap-through, local buckling and bi-stability are investigated, and the feasible design domains for selecting proper lattice and cross-section geometries are identified. In addition, we demonstrate that the proposed design is not restricted to beams, and can be extended to shell structures.

Multi-stable structures are able to achieve significant geometric change and retain specific deformed configurations after the loads have been removed. This reconfiguration property enables, for example, to design metamaterials with tunable features. In this work, a type of multi-stable metastructures exhibiting both level and tilted stable configurations is proposed based on 2D and 3D arrangements of bi-stable elements. The resulting level and tilted configurations are enabled by the rotational compliance, bi-stability and spatial arrangement of unit cells. The bi-stability of the unit cells and multi-stability of the metastructures are demonstrated and characterized by experiments and finite element analysis. Results show that transitions between level stable configurations are symmetric in terms of load–deflection response while switching to the tilted stable configurations leads to asymmetric mechanical responses. The tilted stable configurations are less stable than the level configurations. Moreover, we demonstrate that the level and tilted stable configurations of the metastructure depend on the parallel and serial arrangement of the unit cells.