Miura-ori Pattern Research Articles

Origami electronic membranes as highly shape-morphable mechanical and environmental sensing systems

This work introduces a concept of highly shape-morphable macro-scale origami electronic membranes based on the design and fabrication of flexible electronics and engineering origami. The origami electronic membranes can change shapes, provide multi-modal mechanical and environmental sensing capabilities in room and harsh temperatures, and/or switch functions by mechanical shape reconfiguration. This paper presents the materials, design, and fabrication methods for realizing six origami electronic membranes capable of reconfiguring planar or three-dimensional shapes based on the modified flasher, Kresling, Miura-ori, circular, letter, and Tachi-Miura origami patterns. They can be folded into small, stowed geometries and controllably deployed into larger areas or volumes to cover expanded spaces for spatial sensing, enabling significant shape adaptability for flexible electronics beyond simple stretching or bending. The mechanical and environmental sensing modalities include measuring motions, mechanical strains, temperatures, UV light, and humidity. The results reported here may expand the use of flexible electronics to applications that especially require aggressive shape transitions between a small, folded geometry and a large surface or volume such as deployable sensing systems for space explorations and accessing and monitoring highly confined locations.

Rigid-Foldable Doubly Curved Deployable Reflectors Based on Miura–Ori Pattern

This paper introduces a novel deployable reflector concept which achieves single degree-of-freedom folding of solid doubly curved surfaces. A set of folding kinematics is constructed using the Miura–Ori pattern and the Hoberman linkage to allow compact collision-free stowage of a fully rigid truss-supported solid-surface reflector structure. In this paper, the baseline kinematic architecture is introduced, and a design methodology using Bayesian optimization to systematically obtain optimally stowed geometries is detailed. An example design is carried out to demonstrate the methodology. Optimal parameters are produced, the design space is explored, and a detailed design based on the optimal parameters is made, along with its derivative variants. Finally, a prototype model and quantification of surface errors confirm the validity of resulting designs.

A comprehensive study of a new cylindrical flexible Miura-Ori origami: Kinematics, FEA, and fatigue assessments

In this paper, we introduced a new cylindrical flexible structure incorporating a multi-story origami based on the Miura-Ori pattern and mathematized kinematics. Our experiments validated the finite element simulations as well as the feasibility of the kinematics. We developed a fabrication technique and made a sample to study the feasibility and applicability of the designed structure. Subsequently, we set up a finite element simulation that mirrors the prepared sample. A series of axial folding experiments were carried out to validate the FEM simulation. We have also derived kinematic formulations relating the structure's height, folding angle, and radius. To model and analyze the folding and unfolding mechanisms of this innovative structure, we employed Finite Element Analysis (FEA). In our study, we investigate four main geometric parameters that significantly influence our design's characteristics: crease thickness, number of stories, crease width, and number of vertexes in one story. By varying these design parameters, we systematically examine their impact on key structural attributes such as fatigue life, folding force, and energy absorption. Our findings indicate that reduced crease thickness correlates with lower von-Mises stress and strain, significantly extending the origami design's lifespan. Through our analysis, we identify specific parameter values that maximize fatigue life, ensuring the structural integrity and longevity of the design. Our findings show that increasing the crease width extends the fatigue life dramatically. In conclusion, we summarize the influence of each design parameter on the structure's behavioral characteristics in a comprehensive approach.

Simulation and design of isostatic thick origami structures

Thick origami structures are considered here as assemblies of polygonal panels hinged to each other along their edges according to a corresponding origami crease pattern. The determination of the internal actions in equilibrium with the external loads in such structures is not an easy task, owing to their high degree of static indeterminacy, and the likelihood of unwanted self-balanced internal actions induced by manufacturing imperfections. Here, we present a method for reducing the degree of static indeterminacy which can be applied to several thick origami structures to make them isostatic. The method utilizes sliding hinges, which allow relative translation along the hinge axis, to replace conventional hinges. After giving the analytical description of both types of hinges and describing a rigid folding simulation procedure based on the integration of the exponential map, we present the static analysis of a series of noteworthy examples based on the Miura-ori pattern, the Yoshimura pattern, and the Kresling pattern. Our method, based on kinematic-static duality, provides a novel design paradigm that can be applied for the design and realization of thick origami structures with adequate strength to resist external actions.

Homogenization of non-rigid origami metamaterials as Kirchhoff–Love plates

Origami metamaterials have gained considerable attention for their ability to control mechanical properties through folding. Consequently, there is a need to develop systematic methods for determining their effective elastic properties. This study presents an energy-based homogenization framework for non-rigid origami metamaterials, effectively linking their mechanical treatment with that of traditional materials. To account for the unique mechanics of origami systems, our framework incorporates out-of-plane curvature fields alongside the usual in-plane strain fields used for homogenizing planar lattice structures. This approach leads to a couple-stress continuum, resembling a Kirchhoff–Love plate model, to represent the homogeneous response of these lattices. We use the bar-and-hinge method to assess lattice stiffness, and validate our framework through analytical results and numerical simulations of finite lattices. Initially, we apply the framework to homogenize the well-known Miura-ori pattern. The results demonstrate the framework’s ability to capture the unconventional relationship between stretching and bending Poisson’s ratios in origami metamaterials. Subsequently, we extend the framework to origami lattices lacking centrosymmetry, revealing two distinct neutral surfaces corresponding to bending along two lattice directions, unlike in the Miura-ori pattern. Our framework enables the inverse design of metamaterials that can mimic the unique mechanics of origami tessellations using techniques like topology optimization.

Parametric Analysis on the Static and Modal Response of Folded Metamaterials

Metamaterials have been studied and analyzed in the past three decades because of their outstanding properties. Generally speaking, a metamaterial is a material that exhibits a mechanical behavior that does not depend only on the bulk material but also on the geometrical configuration in which it lies. This aspect leads to the possibility of tuning and engineering the structural response. One of the most interesting properties is the auxetic behavior of metamaterial. An auxetic material shows a global negative Poisson’s ratio. Shock absorption, acoustic dissipation, and shape morphing are some of the most popular employment for auxetic materials. In this article, we focus on the response of folded material under static and dynamic load conditions. Folded materials consist of folding a sheet under specific geometrical constraints. One of the most famous is the Miura-ori pattern, which comes from the origami-folding technique. The geometrical parameters, such as folding angles and edge lengths, play a fundamental role in achieving the desired auxetic behavior. These geometrical parameters define a unit cell that can be stacked into a periodic structure. This article proposes an experimental parametric study of the thickness impact on the auxetic behavior while edge dimensions and folding angles are fixed. The geometrical complexity of the pattern forced us to use additive manufacturing for the specimen fabrication. In particular, we choose Fused Filament Fabrication (FFF) using polymers like ABS and PLA. Digital Image Correlation (DIC) is used for monitoring the displacement and strain fields onto the Miura-ori surface under tensile load. Finally, Time Averaged Speckle Interferometry is employed for evaluating the modal response by using a quasi-full out-of-plane sensitivity setup.

Folding Miura-Ori of Uniform Thickness With One Degree-of-Freedom

Abstract The Miura-ori is an origami pattern with bi-directional folding capable of transforming a large thin sheet into a compact volume with a single degree-of-freedom (DoF). A common Miura-ori pattern consists of identical rigid parallelogram facets that can rotate about the creases without twisting or stretching. However, large gaps along the hinges or uneven surfaces in deployed states are inevitable when thick panels are used. In this paper, the authors add uniform thickness to a Miura-ori tessellation and connect the thick panels by revolute joints on either the top or the bottom facets of the panels for valley creases or mountain creases, respectively. To enable its folding, regular slits are made on some facets not only to remove the excess kinematic constraints but also to accommodate the panel thickness during the folding process. Having made the cuts, we demonstrate that the resultant assembly can fold into a compact package with one DoF. We further notice that although the slits open up during the folding process, they close in the deployed state of the assembly, giving flat and continuous surfaces on both the top and bottom sides. The same method can also be applied to fold the derivatives of the Miura-ori, such as double-corrugated patterns.

Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns

Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.

Deployment dynamics of thick panel Miura-origami

Origami and kirigami folding methods applied to deployable structures have been investigated in many studies, and most of them use approximately zero-thickness materials to follow the paper-folding movement. However, the rigidity and thickness of materials cannot be neglected in aerospace engineering applications, resulting in different kinematic and dynamic characteristics of deployment. This work deals with the deployment dynamics of a typical thick panel Miura origami (Miura-ori). The kinematics of the Miura-ori unit and array are discussed considering the tessellated extension of the Miura-ori pattern, which can be described by the recursively relative movement. Based on the Lagrange's equation, the dynamic equation is determined by generalized force and potential energy. Furthermore, prototypes for Miura-ori unit and array are fabricated, respectively. To measure the dynamic behaviours during deployment, a gravity compensation apparatus is designed and constructed, which can effectively reduce the gravity effect of Miura-ori prototypes. The comparison of the numerical and experimental results validates our dynamic model. Our work provides a recursive dynamic modelling method and experiment apparatus for analysing and testing the deploying dynamic behaviours of tessellated thick-panel origami deployable structures, and the findings can be developed in the other thick-panel origami and kirigami concepts of actual engineering applications in the future.

An origami like 3D patterned cellulose-based scaffold for bioengineering cardiovascular applications

In this work we describe the manufacturing of cellulosic, cell compatible scaffolds with an inherent 3D origami crease pattern for applications in cardiac tissue engineering. Different cellulosic materials were studied, among them cotton linters, fibers obtained from eucalyptus, pine, spruce and lyocell. Formed sheets made of cotton linters were chosen for further study due to the highest biocompatibility and mechanical properties best suited for cardiomyocytes in wet and dry conditions: E - modulus of 0.8 GPa, tensile strength of 4.7 MPa and tensile strength in wet environment of 2.28 MPa. Cell alignment is desired to achieve directional contraction of the cardiac tissue, and several options were investigated to achieve fiber alignment, e.g. a dynamic sheet former and Rapid Köthen sheet former. Although the orientation was minimal, cells cultured on the cellulose fibers grew and aligned along the fibers. Origami inspired crease patterns were applied to the cellulose scaffolds in order to introduce directional flexibility beneficial for cardiac contraction. The transfer of a Miura-ori crease pattern was successfully applied in two ways: folding of the dried sheet between PET foils pre-formed in a 3D printed mold, and in situ wet fiber molding on a 3D-patterned mesh mounted in the sheet former’s sieve section. The latter approach enables upscaling for potential mass production.

Numerical study of the hysteretic behavior of energy dissipation braces based on Miura origami

Miura-ori pattern was adopted to form the tessellation design of slender braces to improve the energy dissipation capacity under the low-cycle repeated loading. The energy dissipation mechanisms of origami energy dissipation braces (OEDBs) and conventional square braces with equal bearing capacity were compared. Finite element models for hysteretic simulation were constructed and analyzed to figure out the influences of various geometrical design parameters on the hysteretic behavior of OEDBs. The results show that the OEDBs have an obvious improvement in the energy dissipation capacity compared to conventional square braces. The influence of parameters on energy dissipation capacity is quite different. The smaller folding angles, smaller aspect ratios, and larger width-to-thickness ratio play positive roles in improving energy dissipation performance rather than elastic stiffness. However, smaller slenderness improves both while the change of in-plane angle is sensitive to the hysteretic performance.

Volume Optimisation of Multi-stable Origami Bellows for Deployable Space Habitats

AbstractOrigami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases. As the bellows unfold, the volume of the origami structure will change significantly, offering potential for use as inflatable deployable structures. This paper presents a geometric study of the volume of multi-stable Miura-ori and Kresling bellows, focusing on their application as deployable space habitats. Such habitats would be compactly stowed during launch, before expanding once in orbit. The internal volume ratio between different deployed states is investigated across the geometric design space. As a case study, the SpaceX Falcon 9 payload fairing is chosen for the transportation of space habitats. The stowed volume and effective deployed volume of the origami space habitats are calculated to enable comparison with conventional habitat designs. Optimal designs for the deployment of Miura-ori and Kresling patterned tubular space habitats are obtained using particle swarm optimisation (PSO) techniques. Configurations with significant volume expansion can be found in both patterns, with the Miura-ori patterns achieving higher volume expansion due to their additional radial deployment. A multi-objective PSO (MOPSO) is adopted to identify trade-offs between volumetric deployment and radial expansion ratios for the Miura-ori pattern.

Deployable structure based on double-layer Miura-ori pattern

With the requirements for improvement of earth observation range and accuracy, large-scale two-dimensional deployable antennas are urgently needed. In this paper, a deployable structure for a planar antenna with one degree of freedom and a flat reflection surface that can realize two-dimensional deployment with a compatible back frame is proposed based on a double-layer Miura-ori pattern. First, an antenna folding scheme with rectangular facets is proposed with the Miura-ori pattern. Through the method for hinge removal and replacement, a deployable antenna mechanism with a flat reflection surface is accomplished. Then, a kinematic model of the deployable structure is established to analyze its kinematic characteristics and prove the equivalence of motion before and after changing the hinges. By converting the rotating pairs between the two layers of origami into cylindrical pairs, a thick-panel form of double-layer origami is constructed. On this basis, a compatible back frame for the planar antenna mechanism is designed and a corresponding prototype is fabricated. The work paves the way to design deployable structures.

Design of deployable circular structures based on Miura origami pattern

A high deploy/fold ratio is essential for space deployable structures to maintain the storage efficiency of the spacecraft. This paper proposes a planar deployable circular structure (DCS) based on the Miura-ori pattern, as well as the design of system parameters and an optimization model for the deploy/fold ratio. In addition, another method for designing curved-surface DCS is proposed that is based on the parallel projection principle. To ensure the structure's foldability and surface accuracy, a mathematical model is established based on the projected vertices on the innermost circle of the target spherical surface. Moreover, suitable numerical design methods for obtaining the vertices of planar and curved-surface DCSs are summarized. Furthermore, the actuation methods for planar and curved-surface deployable structures are presented. The physical prototypes are fabricated, and deployment experiments are conducted to verify the feasibility of the proposed design approach. The novel design of planar and curved-surface DCSs presented in this paper provides a new inspiration for the practical design of deployable space structures.

Origami-Inspired Deployable Space Habitats

Origami is increasingly used as a source of inspiration in a wide variety of disciplines. In this project, we explore cylindrical origami structures, referred to as “origami bellows”, as novel geometries for orbital space habitats. The dimensions of space habitats are limited by the tight mass and volume constraints imposed by launcher payload fairings. Future deployable habitats based on foldable origami bellows have the potential to achieve large volumes when deployed, while being capable of compacting to smaller stowed configurations for launch. To assess the feasibility of such habitat designs, the deployment performance of a selection of bellows was investigated. Bellows formed from Kresling and Miura-ori patterns were considered; both expand axially, but Miura-ori patterns experience an additional radial expansion. Our scope was also limited to patterns which are stable in both the stowed and deployed configurations. Habitats were judged on their internal and effective volume expansions; the latter being adjusted to account for the practicalities of operating within a complex habitat geometry. We find that significant internal and effective volume expansions are achievable, particularly for Miura-ori geometries. Nonetheless, we make the argument for Kresling patterns as a more practical option due to their simpler geometries, despite smaller volume expansions. We find our Kresling geometries to have effective volumes between 2.5 - 3.6 times greater than a conventional habitat launched in a fairing of equal volume. Our work shows that origami-based designs do indeed have potential to greatly outperform current space habitat designs. Keywords: Origami Bellows, Space Habitats, Deployable Structures

Wrinkles, Ridges, Miura-Ori, and Moiré Patterns in MoSe2 Using Neural Networks.

Effects of lateral compression on out-of-plane deformation of two-dimensional MoSe2 layers are investigated. A MoSe2 monolayer develops periodic wrinkles under uniaxial compression and Miura-Ori patterns under biaxial compression. When a flat MoSe2 monolayer is placed on top of a wrinkled MoSe2 layer, the van der Waals (vdW) interaction transforms wrinkles into ridges and generates mixed 2H and 1T phases and chain-like defects. Under a biaxial strain, the vdW interaction induces regions of Miura-Ori patterns in bilayers. Strained systems analyzed using a convolutional neural network show that the compressed system consists of semiconducting 2H and metallic 1T phases. The energetics, mechanical response, defect structure, and dynamics are analyzed as bilayers undergo wrinkle-ridge transformations under uniaxial compression and moiré transformations under biaxial compression. Our results indicate that in-plane compression can induce self-assembly of out-of-plane metasurfaces with controllable semiconducting and metallic phases and moiré patterns with unique optoelectronic properties.

Nonlinear stiffness analysis and programming of a composite origami metamaterial with embedded joint-type metastructures

Origami metamaterials have tremendous application potential in the fields of advanced deployable mechanisms, intelligent robots, and energy absorption devices. In this paper, we embed the flexible joints with metamaterial properties into the origami metamaterial structure, making the origami mechanism have simultaneous geometric nonlinearity and joint stiffness nonlinearity, and investigate the nonlinear stiffness characteristics of this composite metamaterial in detail. To enhance the bearing capacity of the overall structure, the tension spring is mounted to simulate the elastic effect of the crease, and the mechanical metamaterial property of this flexible joint is also revealed theoretically. Based on the kinematics of Miura-ori pattern, the static nonlinear mechanical properties of the composite metastructure are obtained. Besides, the detailed parameter analysis gives an effective validation of the strong design flexibility of the proposed origami mechanism, and the stiffness property programming is realized by tuning structural parameters. Finally, an experimental system is established to test the static mechanical properties of the flexible joint and the origami mechanism, and the high agreement between experimental curves and theoretical results confirms the effectiveness and practicality of the composite metamaterial. This work is helpful for the design of origami metamaterials exploiting their stiffness nonlinearity.

Geometric analyses and experimental characterization of toroidal Miura-ori structures

Origami inspired structures are largely being recognized as efficient deployable structures that can serve multidisciplinary applications. This research focuses on the geometric analyses and quasistatic behavior of toroidal folding patterns based on the four-fold line origami concept. A sequential design process is presented to develop four-fold line toroidal origami structures from a flat sheet of paper, followed by a generalized design algorithm based on the mathematical formulation of the design process. The availability of the geometric design space is calculated considering the limiting values of the design parameters. Geometric analyses is performed to investigate the influence of design parameters on the packaging parameters and availability of the design space. A novel experimental setup is developed, and methodology is introduced to investigate the quasistatic behavior of the single story toroidal patterns. Then, this experimental approach is utilized to characterize the single story toroidal Miura-ori patterns (TMOPs) on the basis of their quasistatic behavior. Moreover, the quasistatic behavior of multi story TMOPs is investigated experimentally.

Experimental study on the flat-wise compression of foldcore sandwich paperboard

Foldcore sandwich structures have aroused considerable research interest in recent years. While foldcores made of metal or composite have been studied extensively, paper-based foldcore are relatively rare. In this paper, we focus on the flat-wise compression properties of foldcore sandwich paperboard with the Miura-ori pattern in the field of packaging and logistics engineering. The flat-wise compression properties and affecting factors of foldcore sandwich paperboard are identified experimentally. Among these factors, the side length ratio (a/b) of the Miura-ori unit significantly influences the deformation mode of the foldcore sandwich paperboard, thus affecting the load-carrying performance and energy-absorption properties. Moreover, the foldcore sandwich paperboard is compared with the conventional corrugated paperboard. The results indicated that although the specific peak stress of foldcore sandwich paperboard and conventional B-flute corrugated paperboard are approximately equal at the same profile angle, the specific energy absorption of the former was 2.06 times higher than the latter. What is more, the specific peak stress and specific energy absorption of the foldcore sandwich paperboard are 1.93 times and 3.24 times higher than those of B-flute corrugated paperboard by merely increasing the sector angle from 60° to 75°. These findings may provide the potential for practical application of paper-based foldcore sandwich panels, thus facilitating the structural design of multilayered cushioning paper pads.

Optimizing geometry for EM performance to design volume-efficient Miura-ori for reflectarray antennas

Trends in the aerospace industry are driving payloads to be smaller and less expensive while yet delivering comparatively large antennas. Deployable reflectarray antennas are often used to meet these demands. The more that a deployable reflectarray fills an allotted volume in the stowed state, the greater the surface area it will realize in the deployed state. Thick, flat-foldable origami designs are therefore excellent design candidates for reflectarray antennas, as they stow as efficiently as possible. This is desirable for antennas as surface area is directly proportional to gain. Gain is also affected by efficiency, which is a function of the geometry of the antenna aperture. As the most efficient rectangular reflectarray profile is a square, this work develops the metrics and relationships that enable an optimization problem seeking to maximize surface area subject to the constraints of an allotted cuboid volume and a deployed aspect ratio of one. The source origami is a modified thickness-accommodating Miura-ori pattern herein termed volume-efficient Miura-ori (VEMO), selected for its ability to fold into a rectangular profile and easily adapt to different aspect ratios. A case study is presented with an allotted 1U CubeSat volume and a panel thickness of 2.5 mm.