Metamaterial with tunable positive to negative Poisson’s ratio inspired by the Saint Andrew’s Cross

Abstract

This paper presents a novel mechanical metamaterial inspired by the geometric form of the Saint Andrew’s Cross (Saltire), designed to exhibit a tunable on-axes Poisson’s ratio ranging from positive to negative values. The metamaterial comprises unit cells constructed from interconnected rotating rigid hexagons and triangles, which deform through coordinated rotation about hinge joints. A theoretical analysis based on kinematic transformations and energy equivalence is conducted to derive closed-form expressions for the on-axes Poisson’s ratios and Young’s moduli. A key parameter—the shape descriptor—governs the deformation behavior and determines whether the metamaterial exhibits auxetic or non-auxetic characteristics over a range of internal angles. The study identifies a critical shape descriptor that yields a constant Poisson’s ratio of − 1, independent of deformation, and enables identical axial stiffnesses. For non-critical geometries, the metamaterial demonstrates sharp directional stiffness contrasts, making it suitable for adaptive structures and anisotropic mechanical filtering. The proposed Saltire-based design broadens the geometrical paradigm for mechanical metamaterials, offering tunability in both auxeticity and stiffness through simple geometric adjustments.