Origami Pattern Research Articles

An ultra-wideband origami microwave absorber

Microwave absorbers have been used to mitigate signal interference, and to shield electromagnetic systems. Two different types of absorbers have been presented: (a) low-cost narrowband absorbers that are simple to manufacture, and (b) expensive wideband microwave absorbers that are based on complex designs. In fact, as designers try to increase the bandwidth of absorbers, they typically increase their complexity with the introduction of several electromagnetic components (e.g., introduction of multi-layer designs, introduction of multiple electromagnetic resonators, etc.,), thereby increasing their fabrication cost. Therefore, it has been a challenge to design wideband absorbers with low cost of fabrication. To address this challenge, we propose a novel design approach that combines origami math with electromagnetics to develop a simple to manufacture ultra-wideband absorber with minimal fabrication and assembly cost. Specifically, we utilize a Tachi–Miura origami pattern in a honeycomb configuration to create the first absorber that can maintain an absorptivity above 90% in a 24.6:1 bandwidth. To explain the ultra-wideband behavior of our absorber, we develop analytical models based on the transmission-reflection theory of electromagnetic waves through a series of inhomogeneous media. The ultra-wideband performance of our absorber is validated and characterized using simulations and measurements.

Energy absorption of metal-composite hybrid tubes with a diamond origami pattern

The metal origami tubes which are employed as energy absorption devices have been widely studied. Because the tubes can deform in a high-performance diamond mode (DM) with lots of creases turning into the traveling plastic hinge lines under axial crushing. However, for the composite origami tube, several large fragments rather than the traveling plastic hinge lines were observed in the axial crushing experiments, which means that the origami pattern cannot trigger the DM. Therefore, in this research, the metal origami tube is introduced on the outside of the composite origami tube, forcing the composite origami tube to deform with the deformation of the metal tube (i.e., the DM). Hence more traveling hinge lines are generated resulting in more fiber and matrix damage, which can effectively improve the energy absorption. The experimental results show that the energy absorption of the composite tube can be greatly improved by about 58.64% in the hybrid tube, compared to the single composite tube. In addition, the parameter studies of the hybrid origami tube indicate that it can deform in the DM in a wide range of geometric parameters.

Discrete symmetries control geometric mechanics in parallelogram-based origami

Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson's ratio Miura-ori origami crease pattern. Here, we develop a formalism for linear compatibility that enables explicit investigation of the interplay between geometric symmetries and functionality in origami crease patterns. We apply this formalism to a particular class of periodic crease patterns with unit cells composed of four arbitrary parallelogram faces and establish that their mechanical response is characterized by an anticommuting symmetry. In particular, we show that the modes are eigenstates of this symmetry operator and that these modes are simultaneously diagonalizable with the symmetric strain operator and the antisymmetric curvature operator. This feature reveals that the anticommuting symmetry defines an equivalence class of crease pattern geometries that possess equal and opposite in-plane and out-of-plane Poisson's ratios. Finally, we show that such Poisson's ratios generically change sign as the crease pattern rigidly folds between degenerate ground states and we determine subfamilies that possess strictly negative in-plane or out-of-plane Poisson's ratios throughout all configurations.

Origami-inspired metamaterials hierarchical structure with tailorable crushing behavior

• A design method of origami-inspired metamaterial hierarchical structure (OMHS) is proposed. • Origami crease patterns are beneficial to improve the crushing stability of the OMHS. • Origami folding and amplitude coefficient tailor the load-carrying capability of the OMHS. • The crushing performance of the OMHS is superior to the conventional hierarchical structure. The global bending deformation hinders the development of the thin-walled structure as an energy absorber. Therefore, a design strategy based on the origami-inspired metamaterial hierarchical structure (OMHS) is proposed to avoid the global bending deformation and improve the crushing behavior of thin-walled structures. The stable progressive deformation is formed in the crushing experiment of the OMHS, owing to the deformation following origami crease patterns. Numerical results show that the OMHS exhibits lower initial stiffness and higher load-carrying capability than conventional straight-wall hierarchical structures (CSHS). Furthermore, the mechanical advantage of the OMHS with high hierarchical order is more prominent. Specifically, the load-carrying capacity and corresponding undulation of 9th order OMHS improve by 48.95% and 121.54% than that of the CSHS, respectively. Furthermore, the crushing behavior of high-order OMHS is programmable based on geometric coefficients φ A and φ e , and thickness coefficient φ t , which positively influences the crushing stability, load-carrying capacity and energy absorption. In addition, the theoretical model is constructed to predict the crushing behavior of the OMHS efficiently. This study is looking forward to providing a novel guide to reinforce the crushing behavior of the hierarchical structure by origami-inspired metamaterial design strategy.

Buckling suppression of a thin-walled Miura-origami patterned tube.

In order to improve energy absorption capacity of tubes under axial compression, this work introduces an octagon tube patterned by curved Miura origami pattern and aims at suppressing global buckling of the tube via an appropriate fold line scheme. By categorizing the fold lines of the tube into two types (hinge-like lines and continuous lines) and allocating them to different positions, four arrangement schemes of the lines are developed. Through numerical comparison in force-displacement curve, stress distribution and lateral deformation capacity among four 3-level patterned tubes under different schemes, Scheme 4 (inclined valley lines as hinge-like lines and the others as continuous lines) is found to outperform the others in suppressing global buckling by reducing the magnitude of lateral deformation by up to 59.9% and by delaying the occurrence of global buckling by up to 35.9% compared with the other schemes. To step further, the scheme is applied in a long tube and geometrically different tubes are compared. The results prove that the scheme is potentially an effective way to alleviate buckling instability of a long tube when appropriately designed.

Designing origami tessellations composed of quadrilateral meshes and degree-4 vertices for engineering applications

Origami-based designs have been successfully adopted to solve engineering problems at different scales of application. This article proposes a method for designing origami tessellations composed of quadrilateral meshes and degree-4 vertices. Crease patterns are generated starting from base units to which are applied tailored generation functions. The theoretical framework is further implemented in a parametric design workflow and automated with the aid of an Interactive Evolutionary Algorithm (IEA). The proposed workflow is a flexible tool that could be applied to design and analyse both rigid and non-rigid foldable origami patterns. The design domain could be investigated without pre-defined design goals and with the support of user-defined performance values.

Maximal origami flip graphs of flat-foldable vertices: properties and algorithms

Flat origami studies straight line, planar graphs $C=(V,E)$ drawn on a region $R\subset\mathbb{R}^2$ that can act as crease patterns to map, or fold, $R$ into $\mathbb{R}^2$ in a way that is continuous and a piecewise isometry exactly on the faces of $C$. Associated with such crease pattern graphs are valid mountain-valley (MV) assignments $\mu:E\to\{-1,1\}$, indicating which creases can be mountains (convex) or valleys (concave) to allow $R$ to physically fold flat without self-intersecting. In this paper, we initiate the first study of how valid MV assignments of single-vertex crease patterns are related to one another via face-flips, a concept that emerged from applications of origami in engineering and physics, where flipping a face $F$ means switching the MV parity of all creases of $C$ that border $F$. Specifically, we study the origami flip graph $\rm{OFG}(C)$, whose vertices are all valid MV assignments of $C$ and edges connect assignments that differ by only one face flip. We prove that, for the single-vertex crease pattern $A_{2n}$ whose $2n$ sector angles around the vertex are all equal, $\rm{OFG}(A_{2n})$ contains as subgraphs all other origami flip graphs of degree-$2n$ flat origami vertex crease patterns. We also prove that $\rm{OFG}(A_{2n})$ is connected and has diameter $n$ by providing two $O(n^2)$ algorithms to traverse between vertices in the graph, and we enumerate the vertices, edges, and degree sequence of $\rm{OFG}(A_{2n})$. We conclude with open questions on the surprising complexity found in origami flip graphs of this type.

Approaches for Minimizing Joints in Single-Degree-of-Freedom Origami-Based Mechanisms

Abstract Origami patterns have been used in the design of deployable arrays. In engineering applications, paper creases are often replaced with surrogate folds by providing a hinge-like function to enable motion. Overconstraint observed in multivertex origami patterns combined with imperfect manufacturing may cause the resulting mechanisms to bind. The removal of redundant constraints decreases the likelihood of binding, may simplify the overall system, and may decrease the actuation force by reducing friction and other resistance to motion. This paper introduces a visual and iterative approach to eliminating redundant constraints in origami-based mechanisms through joint removal. Several techniques for joint removal are outlined and illustrated to reduce overconstraints in origami arrays.

Deformation characteristics and mechanical properties tuning of a non-rigid square-twist origami structure with rotational symmetry

Non-rigid origami patterns could provide more versatile performance than their rigid counterparts in the design of mechanical metamaterials owing to the simultaneous deformation of facets and creases, but their complex deformation modes make quantitative characterization and tuneability of mechanical properties a challenging task. Here, we investigated the tensile behavior of a non-rigid square-twist origami structure with rotational symmetry by combining biaxial tension experiments and finite element modeling. A three-stage deformation process, including tightening, unlocking, and flattening, of the structure was unveiled through a detailed analysis of facet distortion and crease rotation, and the relationship between structure deformation and several key features in the energy, force, and stiffness curve was obtained. Based on the analysis, an empirical model was built to correlate the geometric and material parameters of the structure and its deformation energy, initial peak force, and maximum stiffness, which were further validated through experiments. Using the model, the mechanical properties of the structure can be accurately predicted and tuned based on specific engineering requirements, thereby serving the development of new tuneable mechanical metamaterials based on the family of square-twist origami.

Deployable toroidal structures based on modified Kresling pattern

Origami folding methods are increasingly becoming a vital factor in the advancement of deployable structures. The present study aims to the folding pattern design and deformation analyses of origami based deployable toroidal structures. A novel generalized algorithm is proposed to design six-fold line origami patterns for the development of circumferentially foldable/deployable toroidal structures. The proposed design approach is based on the mathematical optimization of the fold angles to accomplish perfect foldability and closure conditions. The foldability of the designed toroidal origami pattern is verified mathematically as well as by developing physical models. The angular deployment scheme is introduced to analyze the deformation behavior of the toroidal Kresling pattern numerically using pin-jointed wireframe technique. Later, a parametric study is performed to examine the influence of design parameters on the deployment strains under angular loading conditions, followed by a brief discussion about the absence of bistabililty phenomenon in the presented origami patterns. Moreover, the development procedure of paper based models of multi-story deployable toroidal sections is presented, and their shape accuracy is analyzed experimentally.

Kirigami-inspired thick-panel deployable structures

Thick-panel origami has been studied extensively. One of the approaches converts origami creases to simple rotational connections and treats thick-panel origami as assembly of spatial linkages. While structures developed by this approach have one degree of freedom that provide accurate and precise deployment, they often expand to jagged surfaces. In this study, a kirigami-inspired approach, which selectively cuts open some creases in origami patterns, is presented to create deployable surface structures with completely flat surfaces. Starting with a two-vertex origami pattern, we use the theory of spatial linkages to investigate the foldabilities when different mountain–valley assignments are adopted. Combined with a parametric study on the panel thicknesses, we identify a family of deployable two-vertex thick-panel kirigami structures composed of panels of uniform thickness. The slits of the kirigami close completely once deployed. They are subsequently tessellated to form large deployable flat arrays while the kinematic properties are retained. The findings are beneficial for designing deployable structures for engineering applications involving flat panels, e.g., solar panels, shelters, and solid surface antennas.

Energy absorption properties of composite sandwich tubes with pre-folded cores

Composite sandwich tubes have been widely used in aviation and automobile industries due to their high specific mechanical properties. This paper presents an experimental and numerical study on the energy absorption properties of composite sandwich tubes with pre-folded core (CSTPC) based on the full-diamond origami pattern. The CSTPC specimens were fabricated using the hot-press and vacuum-bag molding methods. Axial compression tests were carried out to obtain the mechanical properties of CSTPC with and without the inversion cap. The experiment results showed that CSTPCs with the inversion cap exhibit impressive energy absorption properties. Secondly, the FE modelling method for CSTPC with the inversion cap was developed and validated with the experiment data. An extensive parametric study on CSTPCs with various CSTPC geometries, wall thickness and composite layups and geometries of the inversion cap was conducted. Moreover, CSTPC was compared to the stand-alone straight or pre-folded composite tube and composite sandwich tube with corrugated core. The results showed that CSTPC possesses better energy absorption performance than the stand-alone tubes or the tube with corrugated core.

Fatigue life characterization of hand folded and vacuum formed Kresling origami bellows at 77K

Propellant migration in microgravity is a critical challenge for in-space fuel storage and transfer. Origami fuel bladders are a new design solution to prevent cracking in polymeric materials within the cryogenic regime. This paper explores manufacturing techniques for producing origami bladders as well as the limits of possible thicknesses for origami bladders. Origami bladders are manufactured from polyvinylidene fluoride (PVDF) and polyethylene terephthalate glycol (PETG). Hand folded bladders follow a Kresling bellows origami pattern while the thermoformed samples are prepared using a mold of the Kresling bellows and an EZFORM LV 1827 thermoformer is used to shape the polymeric film. Compressive fatigue testing is carried out within liquid nitrogen to confirm the sample can survive deformation at cryogenic temperatures. Hand folded origami bellows specimens survived 3300+ cycles with minimal signs of degradation, while similar PVDF specimens cracked in fewer than 10 cycles.

Design and kinematic analysis of a rigid-origami-based underwater sampler with deploying-encircling motion

Due to the nondestructive characteristic, the non-contact underwater samplers become important equipment in underwater organism research. This paper proposes a novel underwater sampler with one degree-of-freedom (DOF) deploying-encircling motion based on non-Euclidean rigid origami, and its key factor is the encircling surface origami pattern. The sampler can be deployed and encircle the object gradually from the flat and open configuration to the closed configuration forming an approximate prismatic cavity, and capture organisms without damage. Based on the kinematics of two basic non-Euclidean 4-vertices used in the sampler, the rigid foldability and bifurcation behavior of the origami pattern are analyzed. The bifurcated paths are introduced into the motion transmission path analysis, ensuring the validity of the rigid foldability in all cases. After the bifurcation analysis, the inputs of the pattern are determined. Several performance indexes are evaluated to determine the key parameter. Finally, the drive of the sampler is designed, and the prototype of the sampler is presented and tested for capturing performance in an aquarium.

Performance Study of Origami Crash Tubes Based on Energy Dissipation History

Thin-walled tubes are widely used as energy-absorbing components in traffic vehicles, which can absorb part of the energy in time by using the plastic deformation of the components during collision so as to reduce the damage of the vehicle body and improve the overall safety and reliability of traffic vehicles. The prefolded design of thin-walled tube components can guide it to achieve the ideal energy dissipation performance according to the preset damage path, so the related research based on origami tubes has attracted a lot of attention. Since the geometry of the origami tubes is controlled by many parameters and stress and deformation is a complex nonlinear damage process, most of the previous studies adopted the method of case analysis to carry out numerical simulation and experimental verification of the relevant influence parameters. This paper makes a new exploration of this kind of problem and focuses on solving the related technical problems in three aspects: 1. The automatic model modeling and 3D display based on parameters are proposed; 2. System integration using Python programming to automatically generate the data files of ABAQUS for finite element simulation was realized, and we sorted the finite element analysis results into an artificial intelligence analysis data set; 3. Clustering analysis of the energy consumption history of the data set is carried out using a machine learning algorithm, and the key design parameters that affect the energy consumption history are studied in depth. The sensitivity of the energy absorption performance of the origami tubes with multi-morphology patterns to the crease spacing is studied, and it is shown that the concave–convex crease spacing distribution with a distance larger than 18 mm could be used to activate specific crushing modes. In the optimal case, its initial peak force is reduced by 66.6% compared to uniformly spaced creases, while the average crushing force is essentially the same. Furthermore, this paper finds a new path to optimizing the design of parameters for origami tubes including a multi-morphology origami pattern from the perspective of energy dissipation.

Origami-patterned capacitor with programmed strain sensitivity

Origami patterns have previously been investigated for novel mechanical properties and applications to soft and deployable robotics. This work models and characterizes the mechanical and electrical properties of origami-patterned capacitive strain sensors. Miura-patterned capacitors with different fold angles are fabricated with a silicone body and foil electrodes. The planar strain sensitivity ratio is tunable from 0.2 to 0.5 with fold angles, while all-soft patterns demonstrate low mechanical tunability through fold angle. We conclude by offering recommendations for designing and modeling future origami-patterned soft material sensors.

3D printed deployable origami patterns at intermediate folding configurations for wave guiding applications

Origami-based engineering employs the use of complex reconfigurable structures for a variety of applications in science and engineering. Most origami-inspired structures are designed to be fully deployed, yet wave guiding arrays require deployment to stable intermediate folding configurations to focus waves. Furthermore, current research for origami-inspired wave guiding does not study kinetic and kinematic behavior during compaction and deployment. In this study, the force required to compact the Miura-ori unit cell with compliant joints is investigated for intermediate folding configurations. By starting at intermediate folding angles, the maximum force to reach a fully compact shape can be reduced by over an order of magnitude compared to starting at a flat state.

Experimentally-validated computational modeling and characterization of the quasi-static behavior of functional 3D-printed origami-inspired springs

The presence of Origami patterns in the anatomy of many biological species compels a thorough understanding of their underlying mechanics and possible utilization in man-made systems. Along this line, the past decade has witnessed an increased interest in Origami inspired engineering, where it was shown that foldable and spatially-expandable structures with rich kinematics and unconventional Poisson’s ratio can be created using different Origami patterns. Among those, the Kresling Origami pattern has inspired the design of springs with nonconventional properties. Here, we develop a representative shell-based finite element model for predicting the quasi-static mechanical behavior of a class of 3D printed Kresling Origami springs. We validate the model against experimental data, then use it to generate maps that demarcate regions in the design parameter space into qualitatively different behaviors of the springs. We show that, depending on their design parameters, the springs can exhibit a linear elastic behavior; a nonlinear elastic softening/hardening mono-stable behavior; quasi-zero stiffness behavior; or even a bi-stable behavior. The modularity of these springs, their tunability, and the ability to combine them permits architecturing metamaterials with tunable constitutive laws, which could potentially revolutionize the design of shock absorbers and cushion materials.

Experimental realization of tunable Poisson’s ratio in deployable origami metamaterials

Origami metamaterials are known to display highly tunable Poisson’s ratio depending on their folded state. Most studies on the Poisson effects in deployable origami tessellations are restricted to theory and simulation. Experimental realization of the desired Poisson effects in origami metamaterials requires special attention to the boundary conditions to enable nonlinear deformations that give rise to tunability. In this work, we present a novel experimental setup suitable to study the Poisson effects in 2D origami tessellations that undergo simultaneous deformations in both the applied and transverse directions. The setup comprises a gripping mechanism, which we call a Saint-Venant fixture, to eliminate Saint-Venant end effects during uniaxial testing. Using this setup, we conduct Poisson’s ratio measurements of the Morph origami pattern whose configuration space combines features of the Miura-ori and Eggbox parent patterns. We experimentally observe the Poisson’s ratio sign switching capability of the Morph pattern, along with its ability to display either completely positive or negative values of Poisson’s ratio by virtue of topological transformations. To demonstrate the versatility of the novel setup we also perform experiments on the standard Miura-ori and the standard Eggbox patterns. Our results demonstrate the agreement between the theory, the simulations, and the experiments on the Poisson’s ratio measurement and its tunability in origami metamaterials. The proposed experimental technique can be adopted for investigating other tunable properties of origami metamaterials in static and in dynamic regimes, such as elastic thermal expansion, and wave propagation control.

Toward the Design of Kresling Tower Origami As a Compliant Building Block

Abstract In this paper, the use of the Kresling tower origami as a building block for compliant mechanism design is considered. To help building systems using this origami, models are derived to link the origami pattern geometry to the Kresling tower characteristics. This includes the position of stable configurations, the helical trajectory describing the motion and the orientation of panels during the tower deployment. The provided analytical expressions are helpful to adjust the tower geometry according to desired specification. In addition, an original modification of fold geometry is introduced to modify the tower stiffness. Material removal at specific locations, where maximum fold deformations occur, aims at reducing the actuation force without affecting the kinematics. Experimental evaluation is conducted to assess the relevance of the proposed models and evaluate the impact of fold line modification. The proposed simplified models are precise enough for the synthesis. The capacity to strongly reduce the actuation force, due to the fold line modification, is observed.