Analysis of a 3D Bistable Programmable Metamaterial Mechanism

Programmable metamaterials are designed to tailor mechanical properties and stable configurations through the selection of geometric and material parameters. Here, a two-dimensional auxetic unit is combined with a bistable unit to create a three-dimensional metamaterial mechanism with tunable bistable behaviour. The rotating-triangle architecture of the auxetic unit has a Poisson’s ratio of −1, while the second stable state is governed by the geometry and relative bond stiffnesses of the two units. Bistability occurs when ka/kb<1.25, where ka and kb are the bond stiffnesses of the auxetic and bistable units, respectively. The design parameters determine the second stable state and, in turn, the mechanism’s effective properties. The symmetry of the base cell enables its periodic repetition to form a three-dimensional metamaterial lattice.