安田 博実

We investigate the reconfigurability and tunability of the tessellation of Tachi-Miura Polyhedron (TMP), an origami-based cellular structure composed of bellows-like unit cells. Lattice-based three-dimensional mechanical metamaterials have recently received significant scientific interest due to their superior and unique mechanical performance compared to conventional materials. However, it is often challenging to achieve tunability and reconfigurability from these metamaterials, since their geometry and functionality tend to be pre-determined in the design and fabrication stage. Here, we utilize TMP's highly versatile phase-transforming and tessellating capabilities to design reconfigurable metamaterial architecture with tunable mechanical properties. The theoretical analyses and experiments with heat processing discover the wide range of the in-situ tunability of the metamaterial – specifically orders of magnitude change in effective density, Young's modulus, and Poisson's ratio – after its fabrication within the elastic deformation regime. We also witness a rather unique behavior of the inverse correlation between effective density and stiffness. This mechanical platform paves the way to design the metamaterial that can actively adapt to various external environments.

As an art of paper folding, origami has been widely explored by artists for centuries. Only in recent decades has it gained attention from mathematicians and engineers for its complex geometry and rich mechanical properties. The surge of origami-inspired metamaterials has opened a new window for designing materials and structures. Typically, to build origami structures, a sheet of material is folded according to the creaselines that are marked with compliant mechanisms. However, despite their importance in origami fabrication, such compliant mechanisms have been relatively unexplored in the setting of origami metamaterials. In this study, we explore the relationship between the design parameters of compliant mechanisms and origami mechanical properties. In particular, we employ single hinge crease and Kresling origami, representative examples of rigid and non-rigid origami units, fabricated using a double-stitch perforation compliant mechanism design. We conduct axial compression tests using different crease parameters and fit the result into the bar-hinge origami model consisting of axial and torsional springs. We extract the relationship between the spring coefficients and crease parameters using Gaussian process regression. Our result shows that the change in the crease parameter contributes significantly to each spring element in a very different manner, which suggests the fine tunability of the compliant mechanisms depending on the mode of deformation. In particular, the spring stiffness varies with the crease parameter differently for rigid and non-rigid origami, even when the same crease parameter is tuned. Furthermore, we report that the qualitative static response of the Kresling origami can be tuned between monostable and bistable, or linear and nonlinear, by only changing the crease parameter while keeping the same fold pattern geometry. We believe that our compiled result proffers a library and guidelines for choosing compliant mechanisms for the creases of origami mechanical metamaterials.[Figure not available: see fulltext.]

It is crucial to monitor the wingtip deflection of aircraft in real-time to ensure its aerodynamic functionality and structural safety. Also, the prediction of the wing tip deflection can be highly useful to provide aircraft with improved maneuverability and agile response to sudden events, such as gust and flutter. In this study, we propose a wingtip deflection monitoring/prediction method based on machine learning techniques. Specifically, we employ an aerodynamic solver to simulate an aeroelastic flutter behavior of a fixed-wing, and demonstrate the feasibility of our approach to predict oscillatory wingtip motion due to the flutter. To track and predict the wingtip deflection, we build network architectures composed of convolutional neural networks (CNNs) to analyze optically measured data and recurrent neural networks (RNNs) to process time-series information. As a result, we find the proposed technique is capable of monitoring and predicting wingtip deflection in an accurate and efficient manner. We expect this vision and machine-learning-based technique can complement existing sensor technologies to enhance the safety and maneuverability of aircraft.

The leaf-like origami structure is inspired by geometric patterns found in nature, exhibiting unique transitions between open and closed shapes. With a bistable energy landscape, leaf-like origami is able to replicate the autonomous grasping of objects observed in biological systems such as the Venus flytrap. We show uniform grasping motions of the leaf-like origami, as well as various nonuniform grasping motions that arise from its multitransformable nature. Grasping motions can be triggered with high tunability due to the structure's bistable energy landscape. We demonstrate the self-adaptive grasping motion by dropping a target object onto our paper prototype, which does not require an external power source to retain the capture of the object. We also explore the nonuniform grasping motions of the leaf-like structure by selectively controlling the creases, which reveals various unique grasping configurations that can be exploited for versatile, autonomous, and self-adaptive robotic operations.

Origami-based mechanical metamaterials have recently received significant scientific interest due to their versatile and reconfigurable architectures. However, it is often challenging to account for all possible geometrical configurations of the origami assembly when each origami cell can take multiple phases. Here, we investigate the reconfigurability of a tessellation of origami-based cellular structures composed of bellows-like unit cells, specifically Tachi-Miura Polyhedron (TMP). One of the unique features of the TMP is that a single cell can take four different phases in a rigid foldable manner. Therefore, the TMP tessellation can achieve various shapes out of one original assembly. To assess the geometrical validity of the astronomical number of origami phase combinations, we build a graph-theoretic framework to describe the connectivity of unit cells and to analyze the reconfigurability of the tessellations. Our approach can pave the way to develop a systematic computational tool to design origami-based mechanical metamaterials with tailored properties.

Origami, the ancient art of paper folding, has shown its potential as a versatile platform to design various reconfigurable structures. The designs of most origami-inspired architected materials rely on a periodic arrangement of identical unit cells repeated throughout the whole system. It is challenging to alter the arrangement once the design is fixed, which may limit the reconfigurable nature of origami-based structures. Inspired by phase transformations in natural materials, here we study origami tessellations that can transform between homogeneous configurations and highly heterogeneous configurations composed of different phases of origami unit cells. We find that extremely localized and reprogrammable heterogeneity can be achieved in our origami tessellation, which enables the control of mechanical stiffness and in-situ tunable locking behavior. To analyze this high reconfigurability and variable stiffness systematically, we employ Shannon information entropy. Our design and analysis strategy can pave the way for designing new types of transformable mechanical devices.

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal test beds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wave packets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend effect. Furthermore, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective "impurities."This behavior serves as a new mechanism for reversibly programming the dynamic response of bistable chains.

The ability for materials to adapt their shape and mechanical properties to the local environment is useful in a variety of applications, from soft robots to deployable structures. In this work, we integrate liquid crystal elastomers (LCEs) with multistable structures to allow autonomous reconfiguration in response to local changes in temperature. LCEs are incorporated in a kirigami-inspired system in which squares are connected at their vertices by small hinges composed of LCE-silicone bilayers. These bend and soften as the temperature increases above room temperature. By choosing geometric parameters for the hinges such that bifurcation points in the stability exist, a transition from mono- or tristability to bistability can be triggered by a sufficient increase in temperature, forcing rearrangements of the structure as minima in the energy landscape are removed. We demonstrate temperature-induced propagation of transition waves, enabling local structural changes to autonomously propagate and affect other parts of the structure. These effects could be harnessed in applications in interface control, reconfigurable structures, and soft robotics.

Purpose: Understanding the mechanical properties of current pessaries is important to improve on existing designs and innovate on novel solutions. Our objective was to mechanically characterize the force required to compress ring pessaries into a folded shape. We hypothesized that the force required to fold ring pessaries would scale inversely with the diameter squared. Methods: We conducted a compression test on ring pessaries to analyze their folding behavior using a mechanical universal testing system. Ring pessaries size #1 through #7 (diameters 50.1–86.7 mm) were placed in the testing platform in a vertical orientation with the bending axis in the horizontal plane. An axial load was applied to induce deformation. Results: With application of an axial force, all pessaries first showed in-plane deformation followed by out-of-plane buckling. Increasing force resulted in a transition between in-plane deformation and out-of-plane buckling, during which the pessary began to fold, analogous to classic Euler buckling of columns. This transition was reflected in the loading curve as a sharp change in slope between the initial strain-softening region and a subsequent nearly horizontal plateau region. The force at the transition point ranged from 4.4 N for a size #7 pessary to 23.5 N for a size #1 pessary. The relationship between force and diameter at the transition point appeared to approximate a 1/L2 dependence, where L is the pessary diameter. Conclusions: Pessary mechanics show buckling and folding behavior with a dependence on pessary architecture. The force required to fold ring pessaries scales inversely with the pessary diameter squared.

Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Recently, machine learning techniques have also been employed to learn physics, but one of the formidable challenges is to predict complex dynamics, particularly chaos. Here, we demonstrate the efficacy of quasi-recurrent neural networks in predicting extremely chaotic behavior in multistable origami structures. While machine learning is often viewed as a “black box”, we conduct hidden layer analysis to understand how the neural network can process not only periodic, but also chaotic data in an accurate manner. Our approach shows its effectiveness in characterizing and predicting chaotic dynamics in a noisy environment of vibrations without relying on a mathematical model of origami systems. Therefore, our method is fully data-driven and has the potential to be used for complex scenarios, such as the nonlinear dynamics of thin-walled structures and biological membrane systems.

Deployable structures are typically made of thin membranes and slender elements, which often require foldable – yet stiff – mechanical properties. The use of carbon fiber reinforced polymer (CFRP) composites for such deployable structures has been limited due to the their rigid and unfoldable nature in general. Here, we design, fabricate, and demonstrate foldable – yet stiff – structures made of CFRP composites. To achieve this, we leverage origami design principles based on the Tachi-Miura-Polyhedron (TMP) architecture. To manufacture TMP structures, we devise a unique vacuum-bag-only composite fabrication method by using compliant urethane epoxies impregnated into woven glass fiber layers on which pre-made CFRP tiles are positioned. We show the resulting structures feature self-deployability, high compactness, and deterministic force–displacement characterization. Potential applications of the proposed composite origami are abundant, including deployable habitats for space exploration and disaster relief, deployable solar arrays and antennas, actively-controlled aerodynamic surfaces, and impact mitigation structures.

We experimentally, numerically, and analytically investigate transition waves in a mechanical metamaterial comprising a chain of tristable elements. Transition waves can be initiated from different stable phases within the highly tunable tristable energy landscape. These waves propagate via coupled translational and rotational motion that leads to formation of stationary domain walls if transition waves of incompatible type collide. Since domain formation and propagation is fully reversible, the unique nonlinear behavior could be exploited in new classes of reconfigurable metamaterials.

Periodic cellular structures are widely used in engineering applications due to their lightweight, space-filling, and load-supporting nature. However, the configuration of cellular structures is generally fixed after they are initially built, and it is extremely difficult to change their structural properties—particularly their load-bearing capabilities—in a controllable fashion. Herein, it is shown that volumetric origami cells made of Tachi–Miura polyhedron (TMP) can exhibit in situ transition between flat-foldable and load-bearing states without modifying their predefined crease patterns or hitting the kinematically singular configuration. Theoretical analysis is conducted to study this mechanical bifurcation to establish the design principle, which is verified experimentally by fabricating self-folding TMP prototypes made of paper sheets and heat-shrinking films. The improvement of load-carrying capabilities by 102 is demonstrated by switching the TMP from foldable to load-bearing configurations. These programmable structures can provide practical solutions in various engineering applications, such as deployable space structures, portable architectures for disaster relief, reconfigurable packing materials, and medical devices such as stents.

The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical, and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the origami structure to feel tension first instead of compression under impact. This counterintuitive dynamic mechanism can be used to create a highly efficient-yet reusable-impact mitigating system without relying on material damping, plasticity, or fracture.

We explore unique wave dynamics in a chain of tristable structures, inspired by multistable origami. We specifically focus on the frequency band structure of the chain, and conduct numerical and theoretical analysis. The band gap of the chain can be controlled by switching the stable state of each tristable structure. We also show that if two regions of the chain have different topological properties then wave localization can occur at the interface of the two regions. Interestingly, this interface mode is observed within the band gap. We demonstrate that the interface mode can be altered by leveraging the reconfigurable nature of the tristable structure. Our findings suggest a new strategy for controlling wave propagation in reconfigurable structures, which could be relevant for engineering applications such as energy harvesting.

A novel design of an elastic metamaterial with anisotropic mass density is proposed to manipulate flexural waves at a subwavelength scale. The three-dimensional metamaterial is inspired by kirigami, which can be easily manufactured by cutting and folding a thin metallic plate. By attaching the resonant kirigami structures periodically on the top of a host plate, a metamaterial plate can be constructed without any perforation that degrades the strength of the pristine plate. An analytical model is developed to understand the working mechanism of the proposed elastic metamaterial and the dispersion curves are calculated by using an extended plane wave expansion method. As a result, we verify an anisotropic effective mass density stemming from the coupling between the local resonance of the kirigami cells and the global flexural wave propagations in the host plate. Finally, numerical simulations on the directional flexural wave propagation in a two-dimensional array of kirigami metamaterial as well as super-resolution imaging through an elastic hyperlens are conducted to demonstrate the subwavelength-scale flexural wave control abilities. The proposed kirigami-based metamaterial has the advantages of no-perforation design and subwavelength flexural wave manipulation capability, which can be highly useful for engineering applications including non-destructive evaluations and structural health monitoring.

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.

The goal of this paper is to prove the possibility to design and manufacture novel types of foldable - yet stiff - structures based on the Tachi-Miura-Polyhedron (TMP) origami. This type of origami has received significant attention from the scientific and engineering community due to its unique features such as rigid foldability, high compactness, and tunable stiffness. The kinematics of this TMP structure will be investigated in order to achieve extraordinary mechanical properties in terms of robust deployability. Several prototypes have been tested with hinges made out of both dry and wet fibers, using glass, carbon, and Kevlar materials. While the fabrication process has not been optimized yet, the progress made so far clearly shows that foldable structures are attainable.

The goal of this paper is to construct lightweight, deployable, yet stiff structures made from composite origami. In particular, the deployable origami structures manufactured in this study are based on the Tachi-Miura-Polyhedron (TMP). The TMP is a bellows-like structure that can be stored in a flat state and deployed to a finite volume with defined axial stiffness. The stiffness is highly tunable and depends on several geometric properties as well as the material properties of the crease-lines. The structure can exhibit auxetic behavior among other interesting traits when tuned properly. This study will focus on the manufacturing of this origami utilizing composite materials which can offer a lower weight and higher stiffness solution for constructing the TMP for real world engineering applications. Prototypes are constructed with dry glass fibers to form the crease-lines. Polyurethane resin is then infused to bond the structure together and protect the resin. This research can contribute to the design of origami-based deployable structures in industry and research. The manufacturing process used is relatively simple since it does not require a complex system of moving parts or mechanical connections. Additionally, this structure is hollow and therefore offers a space filling feature which gives it great potential as a space structure or a disaster relief shelter.

Origami has recently received significant interest from the scientific community as a method for designing building blocks to construct metamaterials. However, the primary focus has been placed on their kinematic applications by leveraging the compactness and auxeticity of planar origami platforms. Here, we present volumetric origami cells - specifically triangulated cylindrical origami (TCO) - with tunable stability and stiffness, and demonstrate their feasibility as non-volatile mechanical memory storage devices. We show that a pair of TCO cells can develop a double-well potential to store bit information. What makes this origami-based approach more appealing is the realization of two-bit mechanical memory, in which two pairs of TCO cells are interconnected and one pair acts as a control for the other pair. By assembling TCO-based truss structures, we experimentally verify the tunable nature of the TCO units and demonstrate the operation of purely mechanical one- and two-bit memory storage prototypes.

In this study, we show the formation of frequency band structures in origami-based mechanical metamaterials composed of the Triangulated Cylindrical Origami (TCO). Interestingly, the folding behavior of this structure can exhibit both axial and rotational motions under external excitations. Therefore, these two motions can be strongly coupled with each other, which leads to unique dynamic behavior, particularly wave mixing effects. To analyze the folding behavior of the TCO cells, we model their triangular facets into a network of linear springs. We assemble a 1D chain of multiple TCO unit cells stacked vertically in various arrangements, e.g., changing their stacking sequences and/or orientation angles. We study frequency responses of this system to investigate wave mixing effects between axial and rotational motions under dynamic excitations. This dynamic analysis on the multi-cell structure demonstrates the formation of tunable frequency band structures, which can be manipulated by the arrangement of the unit cells and their initial configurations. By taking advantage of their unique dynamic mechanisms, the origami-based mechanical metamaterials have great potential to be used for controlling structural vibrations in an efficient manner.

In the present work, motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both dispersive shock and rarefaction waves. Depending on the value p of the nonlinearity exponent, we find that both of these possibilities are realizable. We use a quasicontinuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the formation of the dispersive shock, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the highly dispersive nature of the underlying model emerge, which cannot be captured by the quasicontinuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.

We study the kinematics of leaf-out origami and explore its potential usage as multitransformable structures without the necessity of deforming the origami's facets or modifying its crease patterns. Specifically, by changing folding/unfolding schemes, we obtain various geometrical configurations of the leaf-out origami based on the same structure. We model the folding/unfolding motions of the leaf-out origami by introducing linear torsion springs along the crease lines, and we calculate the potential energy during the shape transformation. As a result, we find that the leaf-out structure exhibits distinctive values of potential energy depending on its folded stage, and it can take multiple paths of potential energy during the transformation process. We also observe that the leaf-out structure can show bistability, enabling negative stiffness and snap-through mechanisms. These unique features can be exploited to use the leaf-out origami for engineering applications, such as space structures and architectures.

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber k→±π), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance - enabling full transmission at a particular frequency - in a manner that is analogous to the Ramsauer-Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe almost complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes in granular chains (including disordered ones) with multiple double impurities.

We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.

We investigate unique wave dynamics in origami-based me- chanical metamaterials composed of volumetric 3D origami unit cells. Specifically, we assemble a chain of lattice struc- tures, in which the Tachi-Miura Polyhedron (TMP) is em- ployed as a building block. We conduct two types of theoreti- cal/computational analysis on this origami-based system. One is the dynamic analysis on the TMP unit cell under harmonic excitations. We find that the system transits from linear to non- linear regimes or vice versa, depending on the amplitude of the excitation and the initial configurations of the given geometry. This implies that the origami-based system exhibits intrinsic tun- ability of its dynamic behavior by altering these excitation and geometrical parameters. The other analysis is on a dispersion relationship of mechanical waves propagating through the lat- tice. We analyze a 1D chain of (i) all identical TMP unit cells and (ii) two different unit cells in an alternating arrangement. From this analysis, we show that the origami-based system can create tunable frequency band structures by changing geometrical pa- rameters. By leveraging these unique, tunable wave dynamics, the origami-based mechanical systems have great potential to be used as novel engineering devices that are capable of handling vibrations and impact efficiently.

We investigate the unique mechanical properties of reentrant 3D origami structures based on the Tachi-Miura polyhedron (TMP). We explore the potential usage as mechanical metamaterials that exhibit tunable negative Poisson's ratio and structural bistability simultaneously. We show analytically and experimentally that the Poisson's ratio changes from positive to negative and vice versa during its folding motion. In addition, we verify the bistable mechanism of the reentrant 3D TMP under rigid origami configurations without relying on the buckling motions of planar origami surfaces. This study forms a foundation in designing and constructing TMP-based metamaterials in the form of bellowslike structures for engineering applications.

We design origami-based mechanical metamaterials com- posed of Tachi-Miura Polyhedron (TMP) cells, and we numeri- cally study the propagation of nonlinear waves in them. In or- der to investigate the dynamics of origami structures, we model these TMP-based metamaterials into a simple multi-bar linkage model. By using this model, we find that these TMP cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial condi- tions. By leveraging such tunable strain softening mechanisms, we verify that the origami-based metamaterials can support the propagation of rarefaction waves. These waves feature tensile wave-fronts despite the application of compressive impact to the system. Such unusual characteristics can be exploited to disinte- grate shock waves in a controllable and efficient manner, thereby leading to potential applications in impact mitigation and ab- sorption.

We examine the potential use of origami structures, especially the Tachi-Miura Polyhedron (TMP) which is an origami bellows structure, as mechanical metamaterials. Focusing on the kinematics of its folding, we show that the TMP has unique characteristics, e.g., The Poisson's ratios change from positive to negative depending upon the crease pattern. In addition, we introduce a torsion spring to model the crease line of the TMP in order to study nonlinear wave dynamics. We derive analytical expression of the crease line's motions, where the folding behavior of the crease line provides nonlinear force-displacement responses both in compression and tension. These unusual characteristics lead to potential applications in impact absorption or energy transportation.

In this paper, we examine the folding behaviour of Tachi-Miura polyhedron (TMP) bellows made of paper, which is known as a rigid-foldable structure, and construct a theoretical model to predict the mechanical energy associated with the compression of TMP bellows, which is compared with the experimentally measured energy, resulting in the gap between the mechanical work by the compression force and the bending energy distributed along all the crease lines. The extended Hamilton's principle is applied to explain the gap which is considered to be energy dissipation in the mechanical behaviour of TMP bellows. © 2013 The Author(s) Published by the Royal Society. All rights reserved.