Reconfigurable devices, whose shape can be drastically altered, are central to expandable shelters, deployable space structures, reversible encapsulation systems and medical tools and robots. All these applications require structures whose shape can be actively controlled, both for deployment and to conform to the surrounding environment. While most current reconfigurable designs are application specific, here we present a mechanical metamaterial with tunable shape, volume and stiffness. Our approach exploits a simple modular origami-like design consisting of rigid faces and hinges, which are connected to form a periodic structure consisting of extruded cubes. We show both analytically and experimentally that the transformable metamaterial has three degrees of freedom, which can be actively deformed into numerous specific shapes through embedded actuation. The proposed metamaterial can be used to realize transformable structures with arbitrary architectures, highlighting a robust strategy for the design of reconfigurable devices over a wide range of length scales.

Advances in fabrication technologies are enabling the production of architected materials with unprecedented properties. While most of these materials are characterized by a fixed geometry, an intriguing avenue is to incorporate internal mechanisms capable of reconfiguring their spatial architecture, therefore enabling tunable functionality. Inspired by the structural diversity and foldability of the prismatic geometries that can be constructed using the snapology origami-technique, here we introduce a robust design strategy based on space-filling polyhedra to create 3D reconfigurable materials comprising a periodic assembly of rigid plates and elastic hinges. Guided by numerical analysis and physical prototypes, we systematically explore the mobility of the designed structures and identify a wide range of qualitatively different deformations and internal rearrangements. Given that the underlying principles are scale-independent, our strategy can be applied to design the next generation of reconfigurable structures and materials, ranging from transformable meter-scale architectures to nanoscale tunable photonic systems.

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From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size (1-4). Historically, two main strategies have been pursued to design deployable systems. The first and most common approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract (5-7), occasionally locking in place through bistable elements (8, 9). The second strategy instead, makes use of inflatable membranes that morph into target shapes by means of a single pressure input (10-12). Neither strategy however, can be readily used to provide an enclosed domain able to lock in place after deployment: the integration of protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape (13-15). Here, we draw inspiration from origami, the Japanese art of paper folding, to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the meter-scale, such as arches and emergency shelters, providing a direct pathway for a new generation of large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces. Origami | Multistability | Inflatable structures | Deployable structuresLarge, deployable structures should ideally (i) occupy the minimum possible volume when folded; (ii) be autonomous when deploying; (iii) lock in place after deployment; and (iv) provide a structurally robust shell (if they are designed to define a closed environment). To satisfy all these requirements, we here present a novel approach with roots in the Japanese art of paper folding: origami. Extensively used in robotics (16-20), metamaterials (21-25) and structures (26-30), origami principles have potential to lead to efficient large-scale deployable structures as they offer (i) a versatile crease-based approach to shape design (31-33); (ii) an easy actuation through inflation, if enclosed (34-36); (iii) self-locking capabilities when designed to support multiple energy wells (37-44); and (iv) the possibility to create a protective environment through their faces. While previous origami systems have explored inflatability and multistability separately (34-44), here we show that these two properties can coexist, unlocking an unprecedented design space of meter-scale inflatable structures that harness multistability to maintain their deployed shape without the need for continuous actuation (see schematics in Fig. 1a) Triangular facets as a platform for bistable and inflatable structures. To create inflatable and bistable origami structures, we start by considering a triangular building block ABC and denote with α and β the internal angles enclosed by the edges AB-AC and AB-BC, res...

Self-folding polyhedra have emerged as a viable design strategy for a wide range of applications, with advances largely made through modeling and experimentation at the micro-and millimeter scale. Translating these concepts to larger scales for practical purposes is an obvious next step; however, the size, weight, and method of actuation present a new set of problems to overcome. We have developed large-scale folding polyhedra to rapidly and noninvasively enclose marine organisms in the water column. The design is based on an axisymmetric dodecahedron net that is folded by an external assembly linkage. Requiring only a single rotary actuator to fold, the device is suited for remote operation onboard underwater vehicles and has been fieldtested to encapsulate a variety of delicate deep-sea organisms. Our work validates the use of self-folding polyhedra for marine biological applications that require minimal actuation to achieve complex motion. The device was tested to 700 m, but the system was designed to withstand full ocean depth (11 km) pressures. We envision broader terrestrial applications of rotary-actuated folding polyhedra, ranging from large-scale deployable habitats and satellite solar arrays to small-scale functional origami microelectromechanical systems.