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Abstract Existing Civil Engineering structures have limited capability to adapt their configurations for new functions, non-stationary environments, or future reuse. Although origami principles provide capabilities of dense packaging and reconfiguration, existing origami systems have not achieved deployable metre-scale structures that can support large loads. Here, we established modular and uniformly thick origami-inspired structures that can deploy into metre-scale structures, adapt into different shapes, and carry remarkably large loads. This work first derives general conditions for degree-N origami vertices to be flat foldable, developable, and uniformly thick, and uses these conditions to create the proposed origami-inspired structures. We then show that these origami-inspired structures can utilize high modularity for rapid repair and adaptability of shapes and functions; can harness multi-path folding motions to reconfigure between storage and structural states; and can exploit uniform thickness to carry large loads. We believe concepts of modular and uniformly thick origami-inspired structures will challenge traditional practice in Civil Engineering by enabling large-scale, adaptable, deployable, and load-carrying structures, and offer broader applications in aerospace systems, space habitats, robotics, and more. 

Abstract This paper presents a framework that can transform reconfigurable structures into systems with continuous equilibrium. The method involves adding optimized springs that counteract gravity to achieve a system with a nearly flat potential energy curve. The resulting structures can move or reconfigure effortlessly through their kinematic paths and remain stable in all configurations. Remarkably, our framework can design systems that maintain continuous equilibrium during reorientation, so that a system maintains a nearly flat potential energy curve even when it is rotated with respect to a global reference frame. This ability to reorient while maintaining continuous equilibrium greatly enhances the versatility of deployable and reconfigurable structures by ensuring they remain efficient and stable for use in different scenarios. We apply our framework to several planar four-bar linkages and explore how spring placement, spring types, and system kinematics affect the optimized potential energy curves. Next, we show the generality of our method with more complex linkage systems that carry external masses and with a three-dimensional origami-inspired deployable structure. Finally, we adopt a traditional structural engineering approach to give insight on practical issues related to the stiffness, reduced actuation forces, and locking of continuous equilibrium systems. Physical prototypes support the computational results and demonstrate the effectiveness of our method. The framework introduced in this work enables the stable, and efficient actuation of reconfigurable structures under gravity, regardless of their global orientation. These principles have the potential to revolutionize the design of robotic limbs, retractable roofs, furniture, consumer products, vehicle systems, and more. 

Abstract This work harnesses interpretable machine learning methods to address the challenging inverse design problem of origami-inspired systems. We established a work flow based on decision tree-random forest method to fit origami databases, containing both design features and functional performance, and to generate human-understandable decision rules for the inverse design of functional origami. First, the tree method is unique because it can handle complex interactions between categorical features and continuous features, allowing it to compare different origami patterns for a design. Second, this interpretable method can tackle multi-objective problems for designing functional origami with multiple and multi-physical performance targets. Finally, the method can extend existing shape-fitting algorithms for origami to consider non-geometrical performance. The proposed framework enables holistic inverse design of origami, considering both shape and function, to build novel reconfigurable structures for various applications such as metamaterials, deployable structures, soft robots, biomedical devices, and many more. 

Abstract Thin-walled corrugated tubes that have a bending multistability, such as the bendy straw, allow for variable orientations over the tube length. Compared to the long history of corrugated tubes in practical applications, the mechanics of the bending stability and how it is affected by the cross sections and other geometric parameters remain unknown. To explore the geometry-driven bending stabilities, we used several tools, including a reduced-order simulation package, a simplified linkage model, and physical prototypes. We found the bending stability of a circular two-unit corrugated tube is dependent on the longitudinal geometry and the stiffness of the crease lines that connect separate frusta. Thinner shells, steeper cones, and weaker creases are required to achieve bending bi-stability. We then explored how the bending stability changes as the cross section becomes elongated or distorted with concavity. We found the bending bi-stability is favored by deep and convex cross sections, while wider cross sections with a large concavity remain mono-stable. The different geometries influence the amounts of stretching and bending energy associated with bending the tube. The stretching energy has a bi-stable profile and can allow for a stable bent configuration, but it is counteracted by the bending energy which increases monotonically. The findings from this work can enable informed design of corrugated tube systems with desired bending stability behavior. 

Abstract Origami has great potential for creating deployable structures, however, most studies have focused on their static or kinematic features, while the complex and yet important dynamic behaviors of the origami deployment process have remained largely unexplored. In this research, we construct a dynamic model of a Miura origami sheet that captures the combined panel inertial and flexibility effects, which are otherwise ignored in rigid folding kinematic models but are critical in describing the dynamics of origami deployment. Results show that by considering these effects, the dynamic deployment behavior would substantially deviate from a nominal kinematic unfolding path. Additionally, the pattern geometries influence the effective structural stiffness, and it is shown that subtle changes can result in qualitatively different dynamic deployment behaviors. These differences are due to the multistability of the Miura origami sheet, where the structure may snap between its stable equilibria during the transient deployment process. Lastly, we show that varying the deployment rate can affect the dynamic deployment configuration. These observations are original and these phenomena have not and cannot be derived using traditional approaches. The tools and outcomes developed from this research enable a deeper understanding of the physics behind origami deployment that will pave the way for better designs of origami-based deployable structures, as well as extend our fundamental knowledge and expand our comfort zone beyond current practice. 

Abstract Origami-inspired systems are attractive for creating structures and devices with tunable properties, multiple functionalities, high-ratio packaging capabilities, easy fabrication, and many other advantageous properties. Over the past decades, the community has developed a variety of simulation techniques to analyze the kinematic motions, mechanical properties, and multiphysics characteristics of origami systems. These various simulation techniques are formulated with different assumptions and are often tailored to specific origami designs. Thus, it is valuable to systematically review the state-of-the-art in origami simulation techniques. This review presents the formulations of different origami simulations, discusses their strengths and weaknesses, and identifies the potential application scenarios of different simulation techniques. The material presented in this work aims to help origami researchers better appreciate the formulations and underlying assumptions within different origami simulation techniques, and thereby enable the selection and development of appropriate origami simulations. Finally, we look ahead at future challenges in the field of origami simulation.