Bistable shape-morphing kirigami structures

Shape-morphing structures have attracted broad interest in soft robotics and adaptive surfaces. Previous kirigami and auxetic metamaterials achieved programmable deformation but often relied on complex actuation or lacked mechanical robustness. Recent work introduced bistable auxetic surfaces enabling reversible transformation through conformal mapping and programmable unit design. We present a bistable kirigami metamaterial capable of switching between two stable configurations with enhanced scalability and geometric complexity. The structure is realised by perforating optimised cut patterns into an elastic sheet, forming hexagonal units connected by compliant hinges. A semi-analytical model based on a discrete method predicts deformation and stability, while kinematic and energy analyses capture both local bistability and global deployment. We further propose a design criterion that quantifies the trade-off between rigidity and deployability, enabling the design of more complex morphing surfaces. Unlike previous inverse-design frameworks relying on finite-element databases, our approach is predictive, efficient, and generalizable.