Mechanical performance of negative-stiffness multistable bi-material composites

Architected latticed structural systems, known as metamaterials or metastructures, have recently garnered significant attention due to their superior performance under various loading conditions. This class includes metamaterials exhibiting multistability, characterized by negative stiffness, which enables energy entrapment during transitions between equilibrium states, making them suitable for applications such as lightweight protective systems. In this study, in three folds, we investigate the mechanical performance of a negative stiffness honeycomb metamaterial (NSHM) with unit cells composed of curved double beams. First, the quasi-static compressive response is numerically examined using the finite element method, revealing that this response is independent of the number of cells. Next, we analyze the transient dynamic response of both mono-material NSHMs and bi-material composites, where the stiffeners are replaced by brittle polystyrene, under localized striker and uniform plate impacts. Finally, we present an analytical model for the total potential energy, with solutions obtained through an optimization technique, and validate these results against the numerical simulations. Through these analyses, we study the effects of several parameters influencing multistability. Our findings demonstrate that the bistability ratio significantly impacts the overall response of the honeycomb, and the desired negative stiffness can be achieved with high bistability ratios. Additionally, the contact force peaks resulting from striker impact are found to be independent of the number of constituent elements. The optimized geometry of the lattice is determined through a trade-off between porosity and stiffness, achieved by thicker cell walls.