Stents are flexible structures capable of being folded into small dimensions allowing their passage into the problematic locations in the body and then being expanded. Their prime usage is to treat patients with obstruction at several sites in the body. For example, they are used to open blocked coronary arteries and large veins, to treat obstructions to breathing in the trachea and bronchus, and those in the prostate to allow the passage of urine [1].

Recently, the techniques of origami have become the subject of scientific research. Such methods of folding plates are suitable for practical engineering applications. This paper proposes a novel structure, inspired by thick-panel origami, with hybrid rigid bodies and flexible hinges. Able to be expanded, flipped, and rotated, the waterbomb origami pattern has been chosen to produce a large number of configurations. The mechanism and motion analysis of a single unit and its basic assembly are conducted theoretically and also simulated. An additive fabrication method based on 3D printing makes it a one-step process to achieve a balance between rigidity and flexibility in the structure. Different configurations are demonstrated in three assemblies that exhibit good transformability, reconfigurability, and scalability. With the expansion/packaging ratio ranging from 0.11 to 7.2 in a modular unit, a mechanical metamaterial of negative Poisson’s ratio can be obtained at any spatial size. In addition, our design’s potential for robotic applications is also validated by an adaptable gripper with tendon-driven systems.

Scissor-like structures are commonly composed of two straight rigid supports in a crisscross pattern connected by a pivot at its point of intersection [1]. Opposite angles formed by the supports are equal regardless of the structure’s folded state. Parallelogram linkages have a similar property. Rigid origami can be used to create these structures by combining two identical copies of a 4-crease single-vertex flat-foldable rigid origami, a single 4C, to form a flat-foldable composite structure, a double 4C. In this paper, we prove mathematically that regardless of the folded state of a single-4C, its even dihedral angles are equal, and odd dihedral angles are equal. As a result, the double 4C consists of 2 scissor-like structures. A past method to prove these dihedral angle equalities requires a more complex approach involving rotation matrices using Denavit and Hartenberg parameters [2,3]. This paper will provide a more intuitive method that proves the same equalities. We will also show that a similar construction of the double 4C using thick-panel versions of the single 4C satisfies the same dihedral angle equalities necessary for the formation of parallelogram linkages. The construction of the double 4C can help design self-folding mechanisms and useful metamaterials.

When loaded parallel to the prismatic cells (out-of-plane), honeycombs and re-entrant honeycombs exhibit high initial stiffness and peak force, followed by a force reduction as progressive failure occurs. The high initial peak force and large post-peak force reduction are undesirable for energy absorption purposes. In this study a graded honeycomb structure based on origami is proposed in an effort to lower the peak force, increase the energy absorption capacity and tune the stiffness throughout the loading process. The grading is achieved through a developable origami crease pattern that utilises the typical honeycomb expansion manufacturing technique. The crease pattern has one degree of freedom and is constructed from a repetition of a modified Miura-ori unit. A kinematic study of the crease pattern is completed, highlighting the simple geometric parameters that can be altered to tune the structure. Quasi-static numerical simulations are then used to investigate the interaction between these simple geometric parameters, the energy absorption capacity and the stiffness throughout the loading process. Compared to honeycomb and re-entrant honeycomb tubes, it has been found that a reduction in the peak force, increase in energy absorption capacity and tunable stiffness can be achieved.

In this paper, we investigate and evaluate origami and kirigami patterns that enable folding arrays made from flat rigid panels with uniform thickness into compact stacks. In deployed state, all panels form a completely flat plane; while in folded state, no voids exist within the stack. Two approaches are proposed. The first approach folds an array of identical rectangular panels into compact stacks. By drawing a Hamiltonian circuit over the array, a method of placing revolute joints is presented. By selecting a symmetric Hamiltonian circuit, we show that the array can be folded into two stacks. The second approach is case specific, which folds arrays consisting of square and half square triangular panels into stacks. Three basic units as well as their combinations are proposed, all of which lead to compact folding. Our designs can be applied to package solar panels for aerospace applications.

Functional metamaterials are gradually becoming the frontier of scientific research and industrial applications. Among them, reconfigurable mechanical metamaterial with inbuilt motion capability could result in unusual physical properties such as shape tunability and programmable density and stiffness. Inspired by the transformable cuboid structure that was first investigated by Ron Resch, we proposed a tilted cuboid structure that can fold into a 3D configuration. By designing the individual building units, face angles and tessellation pattern, we are able to construct a series of reconfigurable structures with various shape, twist and permeability feature. Based on our approach, a configuration method to build multi-layer metamaterial is proposed, and it can be generalized to other tilted structures with different building units. The volumetric strains of different models are analyzed, and the result shows the metamaterial has a massive deformation ability as the maximum volume can be four times of the packaged volume. The tilted cuboid structure is highly flexible with variable stiffness and permeability, and can be used to develop metamaterials, large deformation devices and kinetic architectures.

Thin-walled tubes as energy absorption devices are widely in use for their low cost and high manufacturability. Employing origami technique on a tube enables induction of a predetermined failure mode so as to improve its energy absorption efficiency. Here we study the energy absorption of a hexagonal tubular device named the origami crash box numerically and theoretically. Numerical simulations of the quasi-static axial crushing show that the pattern triggers a diamond-shaped mode, leading to a substantial increase in energy absorption and reduction in initial peak force. The effects of geometric parameters on the performance of the origami crash box are also investigated through a parametric study. Furthermore, a theoretical study on the deformation mode and energy absorption of the origami crash box is carried out, and a good match with numerical results is obtained. The origami crash box shows great promise in the design of energy absorption devices.

Resch patterns have a great potential to be utilized in many engineering applications, as they can be folded into curved profiles from planar sheets. They are rigid foldable but with a large number of degrees of freedom (DOF) when there are many units tessellating in the patterns, which constrains the applications due to the difficulty in control the motion symmetrically. In this paper, in order to achieve the single mobility for a limited number of triangular Resch pattern units, the thick-panel technique is employed at each vertex to reduce the DOF to one. Then the compatibility among all the vertices has to be satisfied by the systematical kinematic analysis on the geometric parameters of the Resch pattern and panel thickness. Eventually, two design schemes are obtained to form the one DOF origami structure with doubly-curved intermediate folding configurations, which could be further tessellated into a large pattern for various engineering applications.

In the paper we investigate rigid origami patterns that enables a zero-thickness rigid flat surface to wrap around a square hub with the objective to package solar panels around a cubesat. After a detailed analysis on the rigid foldability of two known patterns, namely the winding membrane and box patterns, we conclude that neither of the patterns can be directly applied to wrap a solar panel, and thus a number of modified patterns are proposed that are capable of rigid folding with one or two degrees of freedom. Their folding sequences are presented and the advantages and shortcomings of the modified patterns are discussed so that designers can make an informed decision when making the selection. Finally we summarised our approach and briefly discussed the possibility to extend our approach to accommodate thick panels.

Large antenna reflectors used in space have to be folded before launching. Silicone rubber is commonly used as antenna material due to its ability to maintain a shape without external supports upon deployment. However, localized vertices could appear during the folding process, which might lead to material yielding and unrecoverable deformation after deployment. In this paper, the cross folding process of a thin elastic sheet, a common folding method in packaging a reflective membrane, was studied numerically with the aim of eliminating material failure in the sheet. The deformation, stress distribution, and peak stress of the sheet and the dependency of those properties on geometrical parameters were systematically investigated. Based on these studies, two methods, i.e., central hole method and central slit method, were explored to reduce the peak stress caused by cross folding. The results showed that a central slit parallel to the first folding crease was the most effective in reducing the peak stress without causing significant damage to the antenna.

Modular origami is a type of origami where multiple pieces of paper are folded into modules, and these modules are then interlocked with each other forming an assembly. Some of them turn out to be capable of large scale shape transformation, making them ideal to create metamaterials with tuned mechanical properties. In this paper, we carry out a fundamental research on 2D modular origami assemblies using mathematical tiling and patterns and mechanism analysis, which leads to the development of various patterns consisting of interconnected quadrilateral modules. Due to the existence of 4R linkages within the patterns, they become transformable, and can be compactly packaged. Moreover, by the introduction of paired modules, we are able to adjust the expansion ratio of the pattern. Additionally, we also show that transformable patterns with higher mobility exist for other polygonal modules. Our findings provide more design flexibility to achieve truly programmable metamaterials.

Functionally graded structures existing in nature can achieve adaptive mechanical properties in response to external loadings through optimizing material distribution. In this paper, a family of origami tubes with systematically varied geometrical parameters are designed and their axial crushing behaviors are analyzed numerically to investigate the concept of inducing graded response through geometrical variation. Three rigid origami patterns are chosen to form the graded origami tubes, and three approaches are adopted to vary tube geometries, including changing the dihedral angle, changing the number of units, and the combinations of them. Numerical results indicate that compared with normal tubes with uniform geometry which have reaction forces with periodic peaks of very close magnitudes, graded origami tubes shows reaction force curves that have different peak values at different stages of deformation. As a result, the amount of axial deformation of the tubes depends on the magnitude of external forces. In the optimal case, a reaction force, the peaks of which are approximately aligned along an ascending straight line, is generated by a tube with both varied dihedral angles and number of units. This work demonstrates that systematic geometrical variation in origami tubes has great potential to trigger graded response.

Deployable structures, whose geometry can change to satisfy practical requirements, have attracted a lot of interests from researchers. And a lot of work has been done on the deployable tubes based on origami patterns. In this paper, three new kinds of deployable tubes based on the well-known kite-shape pattern are proposed. The first kind is generalized kite-shape tubes which are obtained by adding parts composed of parallelogram planes to basic kite-shape tubes. By joining a kite-shape tube or its generalization and a tube with a parallelogram cross section and removing the common sides, a second kind of tubes whose cross section can be a polygon with an odd number of sides is developed. Finally, by misaligning two half kite-shape tubes through a transition zone, a third kind of deployable tubes in which the boundary crease lines between neighboring layers can be on different planes are presented. All the three kinds of new deployable tubes are rigid and have one degree of freedom and are ideal for engineering design and applications.

With the advantage of high adaptability, Miura-origami structure with curvature shows various engineering applications such as a sandwich between two stiff facings with curvature requirements and structural support to form a circular tube. In this research, a forming method of polymer circular tube with single-curved surface origami expressed by five parameters was established and its corresponding theory was solved considering forming rationality in actual manufacturing. The components of circular tube were fabricated by the vacuum forming process and then spliced together. We conducted numerical simulation to analyze the structural performance of the tube with five parameters and shown that these parameters have a great influence on energy absorbed performance. Finally, a male mold of a part with Arc Miura-origami structure was designed and fabricated. The parts with Arc Miura-origami were manufactured using vacuum forming process and then spliced and bonded together into a two-layer tube. This research may provide a method to design and fabricate Miura-origami structure with high efficiency and quality.

Straight-crease origami crash boxes have previously been designed to possess a near optimum failure mode for a tubular energy-absorbing device. This failure mode, termed a ‘complete diamond mode’ (CDM), possesses a low peak force P max and high average force P avg , caused by generation of travelling hinge lines that propagate laterally during crushing. The present study investigates the hypothesis that a curved crease structure could further improve failure characteristics by having a lower P max due to the initially curved corner lobes. An experimental and numerical investigation was conducted using aluminium curved crease origami tubes, with certain curved crease tubes exhibiting the desired CDM and good correspondence seen between experimental and numerical behaviours. A parametric numerical analysis on 45 steel curved crease origami tubes showed a maximum reduction in P max of 67% was observed, which is better than the straight-crease origami crash boxes in this respect. A maximum increase in P avg of 65% was observed, which is worse than straight-crease origami crash boxes. A lower P max was thus achieved as hypothesised, however this improvement came at the expense of a reduction in average force. Curved crease crash boxes are therefore concluded to have minimal benefit over existing straight crease crash box designs.

Foldcore Sandwich structures with high specific strength and specific stiffness will be the aeronautic and astronautic main load-carrying structure materials. Curing process temperature of the Carbon and Kevlar prepreg materials were determined by the best curing process extrapolation method. And then, three dimensional foldcore specimens were manufactured by hot-pressing and piecewise curing molding process. In the compression test, compression force-displacement variation laws and deformation failure modes of the foldcores with different thickness were studied by changing the thickness of core wall. Furthermore, the panel constraints on the properties of compression are studied by pasting panel on the bottom of core and both sides of the core. The researches shows: the compression strength and compression modulus was multiplied increased, and the brittle degree of core was increased with the core wall thickness increasing. The panel restriction for foldcore greatly improved the compression modulus and compression strength.

Thin-walled tubes are widely used as energy absorption devices in automobiles, designed to protect the costly structures and people inside during an impact event through plastic deformation. They show excellent performance under axial loading in terms of weight efficiency, stroke distance and total energy absorption, but also have the disadvantage that the crushing force is not uniform during deformation process, especially with the existence of a high initial peak force. Recently, pattern design on tubular structures has received increasing attention. It has been found that, if the surface of a tube is pre-folded according to an origami pattern, the collapse mode of the tube can be altered, leading to changes in energy absorption performance. In this paper, we present a series of origami patterned tubes with a kite-shape pattern that is constructed by joining two pieces of Miura-ori. First of all, the geometry of the pattern is presented. We develop a theoretical model to predict the energy absorption associated with the axial crushing of the patterned tubes and derive a mathematical formula to calculate the mean crushing force accordingly. Secondly, a family of origami tubes with various profiles are designed, and their performances subjected to quasi-static axial crushing are numerically investigated. A parametric study is also conducted to establish the relationship between the pre-folded angle of the pattern and the initial peak force as well as the mean crushing force. Numerical results show that introducing patterns to thin-walled tubes offers three advantages in comparison with conventional tubes, i.e., a lower initial peak force, a more uniform crushing load, and a stable and repeatable collapse mode. A 36.0% increase in specific energy absorption and 67.2% reduction in initial peak force is achieved in the optimum case. The new origami patterned tubes show great promise as energy absorption devices.