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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.

Metamaterials are artificially structured materials with unusual properties, such as negative Poisson's ratio, acoustic band gap, and energy absorption. However, metamaterials made of conventional materials lack tunability after fabrication. Thus, active metamaterials using magneto-mechanical actuation for untethered, fast, and reversible shape configurations are developed to tune the mechanical response and property of metamaterials. Although the magneto-mechanical metamaterials have shown promising capabilities in tunable mechanical stiffness, acoustic band gaps, and electromagnetic behaviors, the existing demonstrations rely on the forward design methods based on experience or simulations, by which the metamaterial properties are revealed only after the design. Considering the massive design space due to the material and structural programmability, a robust inverse design strategy is desired to create the magneto-mechanical metamaterials with preferred tunable properties. In this work, we develop an inverse design framework where a deep residual network replaces the conventional finite-element analysis for acceleration, realizing metamaterials with predetermined global strains under magnetic actuations. For validation, a direct-ink-writing printing method of the magnetic soft materials is adopted to fabricate the designed complex metamaterials. The deep learning-accelerated design framework opens avenues for the designs of magneto-mechanical metamaterials and other active metamaterials with target mechanical, acoustic, thermal, and electromagnetic properties.

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.

Foldable structures have been of great interest due to their ability to reduce in size from deployed to folded state, enabling easier storage in scenarios with space constraints such as aerospace and medical applications. Hexagonal structural components have been of interest, due to their ability to tessellate, or cover without gap, 2D and 3D surfaces. However, the study on effective folding strategies for hexagon-based structures and the hexagon geometry itself is limited. Here, we report a strategy of snap-folding hexagonal rings, to result in folded states with only 10.6% the initial area of a single ring. Motivated by this significant packing, we utilize a combination of experiments and finite element analysis to study effective folding strategies and packing abilities of various 2D and 3D hexagonal ring assemblies, with structures that can be folded to 1.5% and 0.4% of their initial area and volume, respectively. The effect of geometric parameters of hexagonal rings on the mechanical stability of their assemblies is investigated. Additionally, the instabilities of rings can be utilized to facilitate the automatic deployment of folded ring assemblies under small perturbations. Furthermore, an assembly with rigid functional panels is explored to demonstrate the functionality and design space for hexagonal ring assemblies. With such significant demonstrated area and volume changes upon snap-folding, it is anticipated that hexagonal ring assemblies could inspire future aerospace or biomedical designs, where reconfiguration and large packing are required.

Biomimetic soft robotic crawlers have attracted extensive attention in various engineering fields, owing to their adaptivity to different terrains. Earthworm-like crawlers realize locomotion through in-plane contraction, while inchworm-like crawlers exhibit out-of-plane bending-based motions. Although in-plane contraction crawlers demonstrate effective motion in confined spaces, miniaturization is challenging because of limited actuation methods and complex structures. Here, we report a magnetically actuated small-scale origami crawler with in-plane contraction. The contraction mechanism is achieved through a four-unit Kresling origami assembly consisting of two Kresling dipoles with two-level symmetry. Magnetic actuation is used to provide appropriate torque distribution, enabling a small-scale and untethered robot with both crawling and steering capabilities. The crawler can overcome large resistances from severely confined spaces by its anisotropic and magnetically tunable structural stiffness. The multifunctionality of the crawler is explored by using the internal cavity of the crawler for drug storage and release. The magnetic origami crawler can potentially serve as a minimally invasive device for biomedical applications.

Synthetic biomarkers, exogenous probes that generate molecular reporters, represent an emerging paradigm in precision diagnostics with applications across infectious and noncommunicable diseases. These methods use multiplexing strategies to provide tools that are both sensitive and specific. However, the field of synthetic biomarkers has not benefited from molecular strategies such as DNA-barcoding due to the susceptibility of nucleic acids in vivo. Herein, we exploit chemically-stabilized DNAs to tag synthetic biomarkers and produce diagnostic signals via CRISPR nucleases. Our strategy capitalizes on disease-associated, protease-activated release of nucleic acid barcodes and polymerase-amplification-free, CRISPR-Cas-mediated barcode detection in unprocessed biofluids. In murine cancer models, we show that these DNA-encoded nanosensors can noninvasively detect and monitor disease progression, and demonstrate that nuclease amplification can be harnessed to convert the readout to a point-of-care tool. This technique combines specificity with ease of use to offer a new platform to study human disease and guide therapeutic decisions.

Through experiment and simulation, we study a kind of deployable thin circular ring that can be folded into three small loops. Parametric study is conducted on the ring to study the geometric parameters that can influence ring’s buckling .We also explore the rings with other shapes , such as elliptical rings, rectangular rings. Some applications basing on these studies are shown in this paper.