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Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures. 

One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant trunk is an object of fascination for biologists, physicists, and children alike. Its versatility relies on the intricate interplay of multiple unique physical mechanisms and biological design principles. Here, we explore these principles using the theory of active filaments and build, theoretically, computationally, and experimentally, a minimal model that explains and accomplishes some of the spectacular features of the elephant trunk. 

Abstract Origami has emerged as a powerful mechanism for designing functional foldable and deployable structures. Among various origami patterns, a large class of origami exhibits rotational symmetry, which possesses the advantages of elegant geometric shapes, axisymmetric contraction/expansion, and omnidirectional deployability, etc. Due to these merits, origami with rotational symmetry has found widespread applications in various engineering fields such as foldable emergency shelters, deformable wheels, deployable medical stents, and deployable solar panels. To guide the rational design of origami-based deployable structures and functional devices, numerous works in recent years have been devoted to understanding the geometric designs and mechanical behaviors of rotationally symmetric origami. In this review, we classify origami structures with rotational symmetry into three categories according to the dimensional transitions between their deployed and folded states as three-dimensional to three-dimensional, three-dimensional to two-dimensional, and two-dimensional to two-dimensional. Based on these three categories, we systematically review the geometric designs of their origami patterns and the mechanical behaviors during their folding motions. We summarize the existing theories and numerical methods for analyzing and designing these origami structures. Also, potential directions and future challenges of rotationally symmetric origami mechanics and applications are discussed. This review can provide guidelines for origami with rotational symmetry to achieve more functional applications across a wide range of length scales. 

Abstract Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from the snap-folding mechanism. In general, polygonal rings with rationally designed geometric parameters can fold into compacted three-loop configurations with curved segments, which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects their folded configurations. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find it is possible to reverse the process by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a straight-line looped pattern with “zero” area. This realizes extreme packing. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behavior, folded configurations, and packing of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency. 

Abstract Elephant trunks are capable of complex, multimodal deformations, allowing them to perform task‐oriented high‐degree‐of‐freedom (DOF) movements pertinent to the field of soft actuators. Despite recent advances, most soft actuators can only achieve one or two deformation modes, limiting their motion range and applications. Inspired by the elephant trunk musculature, a liquid crystal elastomer (LCE)‐based multi‐fiber design strategy is proposed for soft robotic arms in which a discrete number of artificial muscle fibers can be selectively actuated, achieving multimodal deformations and transitions between modes for continuous movements. Through experiments, finite element analysis (FEA), and a theoretical model, the influence of LCE fiber design on the achievable deformations, movements, and reachability of trunk‐inspired robotic arms is studied. Fiber geometry is parametrically investigated for 2‐fiber robotic arms and the tilting and bending of these arms is characterized. A 3‐fiber robotic arm is additionally studied with a simplified fiber arrangement analogous to that of an actual elephant trunk. The remarkably broad range of deformations and the reachability of the arm are discussed, alongside transitions between deformation modes for functional movements. It is anticipated that this design and actuation strategy will serve as a robust method to realize high‐DOF soft actuators for various engineering applications.