Hiromi Yasuda

Formation of rarefaction waves in origami-based metamaterials

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.

Folding behaviour of Tachi-Miura polyhedron bellows.

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 Hamiltons principle is applied to explain the gap which is considered to be energy dissipation in the mechanical behaviour of TMP bellows.

Scattering of Waves by Impurities in Precompressed Granular Chains

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.

Multitransformable Leaf-Out Origami With Bistable Behavior

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. [DOI: 10.1115/1.4031809]

Dial-in Topological Metamaterials Based on Bistable Stewart Platform

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.

Emergence of dispersive shocks and rarefaction waves in power-law contact models

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.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 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 quasi-continuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the shock formation, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the discrete nature of the underlying model emerge that cannot be captured by the quasi-continuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.

Origami-based tunable truss structures for non-volatile mechanical memory operation

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.Origami is a popular method to design building blocks for mechanical metamaterials. Here, the authors assemble a volumetric origami-based structure, predict its axial and rotational movements during folding, and demonstrate the operation of mechanical one- and two-bit memory storage.

Kirigami-based Elastic Metamaterials with Anisotropic Mass Density for Subwavelength Flexural Wave Control

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.

Tunable wave propagation in origami-based reconfigurable mechanical metamaterials (Conference Presentation)

We investigate nonlinear wave dynamics in origami-based mechanical metamaterials composed of origami-based structures, specifically the Triangulated Cylindrical Origami (TCO). The TCO structure shows coupling behavior between longitudinal and rotational motions. One of the unique features of the TCO is that the unit cell can exhibit mono- or bistable behavior selectively, which is determined by initial configurations such as height and rotational angle. In this study, we first fabricate physical prototypes made of paper sheets, and conduct compression tests on the prototypes to verify this unique tunable mono-/bistable features. By utilizing this tunability, we design a 1D chain of the TCO unit cells in which mono-/bistable behaviors of each unit cell can be altered by geometric parameters. Then, we analyze wave propagation in this origami-based system numerically by applying impact to the end of the chain. When the monostable configuration is selected for all of the unit cells, our numerical analysis shows that the application of compressive impact creates a tensile solitary wave propagating ahead of the initial compressive wave. In addition, the wave speed of this tensile solitary wave can be manipulated by the configurations of the TCO unit cells. These unique tunable static/dynamic behaviors can be exploited to design engineering devices which can mitigate impact in an efficient manner.

Topologically tunable metamaterial based on bi-stable Stewart platform (Conference Presentation)

The discovery of topological insulators in materials science revolutionized the concept of wave propagation by giving rise to the existence of edge modes that are immune to backscattering. Similarly, the tunability in waveguiding – including in-situ frequency modifications and path designation – can be highly useful in manipulating energy flow, which still remains an open challenge. Here we investigate topologically tunable mechanical metamaterials based on the quantum valley hall effect (QVHE) by utilizing the bi-stable Stewart platform (SP). Generally, topologically protected wave propagation can leverage two physical mechanisms: the quantum hall effect (QHE) and the quantum spin hall effect (QSHE). Compared to the QHE and the QSHE, the QVHE exploited in this study maintains the time reversal symmetry and can be achieved by using a relatively simple, passive system with one degree-of-freedom. The tunable system we propose and investigate in this study is made of a two-dimensional hexagon crystal and is composed of SPs at nodes connected by linear springs. Each building block can exhibit one of the two stable states of the SP, so that the C6 inversion symmetry of the lattice is broken while C3 symmetry is reserved. By changing the sequence of the bi-stable state in the SP, we can formulate two kinds of unit cells – marked as A and B – with different topological properties. Berry curvatures as well as corresponding eigenmodes are obtained to demonstrate the topological conversion between the two lattices. Then we conduct super-cell analysis by forming a 1-by-20 array of A and B unit cells. Band structure of the super-cell indicates the existence of edge modes over the while band gap, which appear at the interface of A and B unit cells. Based on this tunable property of bi-stable SP, we can easily form S-type and L-type (60 and 120 degree bents) topological paths in the 40-by-40 lattices without breaking the original geometry parameters. We then conduct the numerical simulations with these topological wave guides to verify the topological protection of the valley hall edge states from backscattering. The tunable system we proposed in this paper may pave a possible way to achieving tunability of topological metamaterials.