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Abstract In recent decades, origami has been explored to aid in the design of engineering structures. These structures span multiple scales and have been demonstrated to be used toward various areas such as aerospace, metamaterial, biomedical, robotics, and architectural applications. Conventionally, origami or deployable structures have been actuated by hands, motors, or pneumatic actuators, which can result in heavy or bulky structures. On the other hand, active materials, which reconfigure in response to external stimulus, eliminate the need for external mechanical loads and bulky actuation systems. Thus, in recent years, active materials incorporated with deployable structures have shown promise for remote actuation of light weight, programmable origami. In this review, active materials such as shape memory polymers (SMPs) and alloys (SMAs), hydrogels, liquid crystal elastomers (LCEs), magnetic soft materials (MSMs), and covalent adaptable network (CAN) polymers, their actuation mechanisms, as well as how they have been utilized for active origami and where these structures are applicable is discussed. Additionally, the state‐of‐the‐art fabrication methods to construct active origami are highlighted. The existing structural modeling strategies for origami, the constitutive models used to describe active materials, and the largest challenges and future directions for active origami research are summarized. 

Abstract Liquid crystal elastomers (LCE) are appealing candidates among active materials for 4D printing, due to their reversible, programmable and rapid actuation capabilities. Recent progress has been made on direct ink writing (DIW) or Digital Light Processing (DLP) to print LCEs with certain actuation. However, it remains a challenge to achieve complicated structures, such as spatial lattices with large actuation, due to the limitation of printing LCEs on the build platform or the previous layer. Herein, a novel method to 4D print freestanding LCEs on‐the‐fly by using laser‐assisted DIW with an actuation strain up to −40% is proposed. This process is further hybridized with the DLP method for optional structural or removable supports to create active 3D architectures in a one‐step additive process. Various objects, including hybrid active lattices, active tensegrity, an actuator with tunable stability, and 3D spatial LCE lattices, can be additively fabricated. The combination of DIW‐printed functionally freestanding LCEs with the DLP‐printed supporting structures thus provides new design freedom and fabrication capability for applications including soft robotics, smart structures, active metamaterials, and smart wearable devices. 

Origami folding and thin structure buckling are intensively studied for structural transformations with large packing ratio for various biomedical, robotic, and aerospace applications. The folding of circular rings has shown bistable snap‐through deformation under simple twisting motion and demonstrates a large area change to 11% of its undeformed configuration. Motivated by the large area change and the self‐guided deformation through snap‐folding, it is intended to design ring origami assemblies with unprecedented packing ratios. Herein, through finite‐element analysis, snap‐folding behaviors of single ring with different geometries (circular, elliptical, rounded rectangular, and rounded triangular shapes) are studied for ring origami assemblies for functional foldable structures. Geometric parameters' effects on the foldability, stability, and the packing ratio are investigated and are validated experimentally. With different rings as basic building blocks, the folding of ring origami assemblies including linear‐patterned rounded rectangular rings, radial‐patterned elliptical rings, and 3D crossing circular rings is further experimentally demonstrated, which show significant packing ratios of 7% and 2.5% of the initial areas, and 0.3% of the initial volume, respectively. It is envisioned that the reported snap‐folding of origami rings will provide alternative strategies to design foldable/deployable structures and devices with reliable self‐guided deformation and large area change.