Thin sheets have long been known to experience an increase in stiffness when they are bent, buckled, or assembled into smaller interlocking structures. We introduce a unique orientation for coupling rigidly foldable origami tubes in a “zipper” fashion that substantially increases the system stiffness and permits only one flexible deformation mode through which the structure can deploy. The flexible deployment of the tubular structures is permitted by localized bending of the origami along prescribed fold lines. All other deformation modes, such as global bending and twisting of the structural system, are substantially stiffer because the tubular assemblages are overconstrained and the thin sheets become engaged in tension and compression. The zipper-coupled tubes yield an unusually large eigenvalue bandgap that represents the unique difference in stiffness between deformation modes. Furthermore, we couple compatible origami tubes into a variety of cellular assemblages that can enhance mechanical characteristics and geometric versatility, leading to a potential design paradigm for structures and metamaterials that can be deployed, stiffened, and tuned. The enhanced mechanical properties, versatility, and adaptivity of these thin sheet systems can provide practical solutions of varying geometric scales in science and engineering.

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Integrating origami principles within traditional microfabrication methods can produce shape morphing microscale metamaterials and 3D systems with complex geometries and programmable mechanical properties. However, available micro-origami systems usually have slow folding speeds, provide few active degrees of freedom, rely on environmental stimuli for actuation, and allow for either elastic or plastic folding but not both. This work introduces an integrated fabrication-design-actuation methodology of an electrothermal micro-origami system that addresses the above-mentioned challenges. Controllable and localized Joule heating from electrothermal actuator arrays enables rapid, large-angle, and reversible elastic folding, while overheating can achieve plastic folding to reprogram the static 3D geometry. Because the proposed micro-origami do not rely on an environmental stimulus for actuation, they can function in different atmospheric environments and perform controllable multi-degrees-of-freedom shape morphing, allowing them to achieve complex motions and advanced functions. Combining the elastic and plastic folding enables these micro-origami to first fold plastically into a desired geometry and then fold elastically to perform a function or for enhanced shape morphing. The proposed origami systems are suitable for creating medical devices, metamaterials, and microrobots, where rapid folding and enhanced control are desired.

Thin sheets can be assembled into origami tubes to create a variety of deployable, reconfigurable and mechanistically unique three-dimensional structures. We introduce and explore origami tubes with polygonal, translational symmetric cross-sections that can reconfigure into numerous geometries. The tubular structures satisfy the mathematical definitions for flat and rigid foldability, meaning that they can fully unfold from a flattened state with deformations occurring only at the fold lines. The tubes do not need to be straight and can be constructed to follow a nonlinear curved line when deployed. The cross-section and kinematics of the tubular structures can be reprogrammed by changing the direction of folding at some folds. We discuss the variety of tubular structures that can be conceived and we show limitations that govern the geometric design. We quantify the global stiffness of the origami tubes through eigenvalue and structural analyses and highlight the mechanical characteristics of these systems. The two-scale nature of this work indicates that, from a local viewpoint, the crosssections of the polygonal tubes are reconfigurable while, from a global viewpoint, deployable tubes of desired shapes are achieved. This class of tubes has potential applications ranging from pipes and microrobotics to deployable architecture in buildings.

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