Hierarchical Bistability: Reprogramming Global Bistability through Local Bistability

Bistability is a widespread phenomenon observed in both natural and engineered systems, from nanoscale proteins to meter-scale space structures. Over the past two decades, this concept has been embedded into elastic architectures, enabling a wide range of applications, including shape reconfiguration, energy trapping, mechanical logic operations, and reprogrammable phononic bandgaps. In the existing literature, bistability can occur at either the local level of the repeating unit or across the global finite-tessellation scale. A locally bistable transition typically does not result in macroscopic strain, as opposed to a globally bistable transition. In most existing architectures, we observe local and global bistability as intrinsically separate and occurring at their own length scale with no mutual interdependence.

Here, we present a class of architectures that exhibit hierarchical bistability, where the global bistable characteristics can be reprogrammed in situ by leveraging local bistable transitions. Through computational and experimental methods, we demonstrate the emergence of hierarchical bistability in one-dimensional metamaterial arcs, planar linkages, and three-dimensional origami and shell systems, achieving reprogrammable snap-through forces, adjustable shape reconfigurations, and tunable transition paths. Embodying hierarchical bistability in reprogrammable architectures could serve as a platform for developing multifunctional mechanical actuators and switches.