Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence

Multistable mechanical metamaterials are materials that have multiple stable configurations. The geometrical changes caused by the transition of the metamaterial from one stable state to another, could be exploited to obtain multifunctional and programmable materials. As the stimulus amplitude is varied, a multistable metamaterial goes through a sequence of stable configurations. However, this sequence (which we will call the deformation sequence) is unpredictable if the metamaterial consists of identical unit cells. This paper proposes to use small variations in the unit cell geometry to obtain a deterministic deformation sequence for one type of multistable metamaterial that consists of bistable unit cells. Based on an analytical model for a single unit cell and on the minimization of the total strain energy, a rigorous theoretical model is proposed to analyze the nonlinear mechanics of this type of metamaterials and to inform the designs. The proposed theoretical model is able to accurately predict the deformation sequence and the stress–strain curves that are observed in the finite-element simulations with an elastic constitutive model. A deterministic deformation sequence that matches the sequence predicted by the theory and finite-element simulations is obtained in experiments with 3D-printed samples. Furthermore, an excellent quantitative agreement between simulations and experiments is obtained once a viscoelastic constitutive model is introduced in the finite-element model.