Multi-stable metastructure with multi-layer and multi-degree of freedom: A numerical and experimental investigation.

[Display omitted] • A family of multi-layer multistable metastructures is proposed that can realize deformation with multiple degrees of freedom, benefiting from the single-layer unit that is capable of inclining a certain angle in four directions. • The inclined stable state is triggered by the lateral compression, and the transitions between different stable states exhibit different load–displacement responses. • The load–displacement responses of double-layer units are the superposition of those of single-layer units. • The planar or spatial bending postures are realized in the multi-layer, multistable metastructures. This paper proposes a family of multi-stable metastructures with multiple layers, which possess the capability of multi-degree of freedom deformations. In its single layer, four preshaped beams connecting two frames are employed as the main component for the design of multi-stable metastructures. Compared with the traditional flat state obtained by axial compression when all beams snap through, four inclined stable states are easy to trigger by lateral compression at a local position when two adjacent beams snap through. The transitions between these states are studied by both experiments and numerical simulation. The transition to inclined states requires less energy than the transition to the flat state. Different trends of load–displacement responses are associated with loading positions and transitions. A parametric analysis is performed to illustrate the relationship between the stability of inclined states and critical parameters, such as span, apex height, and thickness. Two types of hourglass double-layer units are designed and studied through experiments. The continuous transitions in two steps or three steps are observed, and the load–displacement response is the accumulation of responses from each single layer. At last, two multi-layer structures with multi-stability have been developed to demonstrate their deformation capability in multiple directions through multiple steps. [ABSTRACT FROM AUTHOR]