Formation of rarefaction waves in origami-based metamaterials

Yasuda, Hiromi; Chong, Christopher; Charalampidis, E. G.; Kevrekidis, P. G.; Yang, Jinkyu

doi:10.1103/physreve.93.043004

Cited by 67 publications

(58 citation statements)

References 28 publications

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“…Nevertheless, studying the dynamics of folding is still a nascent field and there are only a few researches conducted in this area. One study by Yasuda et al examined the nonlinear elastic wave propagation in a multiple degree‐of‐freedom origami material consisting of TMP modules . They examined the formation of rarefaction waves due to the geometry‐induced elastic nonlinearity of TMP modules, and explored the feasibility of using such nonlinear wave propagation for tunable vibration and impact mitigating.…”

Section: Folding Induced Mechanical Propertiesmentioning

confidence: 99%

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

et al. 2018

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devices, [26,27] to small-scale nano- [28][29][30] and DNA origamis. [31] A common theme in these studies is to exploit the sophisticated shape transformations from folding. For example, an origami robot is typically fabricated in a 2D flat configuration and then folded into the prescribed 3D shape to perform its tasks. The origamis have been treated essentially as linkage mechanisms in which rigid facets rotate around hingelike creases (aka "rigid-folding origami"). Elastic deformation of the constituent sheet materials or the dynamics of folding are often neglected. Such a limitation in scope indeed resonates the origin of this field, that is, folding was initially considered as a topic in geometry and kinematics.However, the increasingly diverse applications of origami require us to understand the force-deformation relationship and other mechanical properties of folded structures. Over the last decade, studies in this field started to expand beyond design and kinematics and into the domain of mechanics and dynamics. Catalyzed by this development, a family of architected origami materials quickly emerged (Figure 1). These materials are essentially assemblies of origami sheets or modules with carefully designed crease patterns. The kinematics of folding still plays an important role in creating certain properties of these origami materials. For example, rigid folding of the classical Miura-ori sheet induces an in-plane deformation pattern with auxetic properties (aka negative Poisson's ratios). [32,33] However, elastic energy in the deformed facets and creases, combined with their intricate spatial distributions, impart the origami materials with a rich list of desirable and even unorthodox properties that were never examined in origami before. For example, the Ron-Resch fold creates a unique tri-fold structure where pairs of triangular facets are oriented vertically to the overall origami sheet and pressed against each other. Such an arrangement can effectively resist buckling and create very high compressive load bearing capacity. [34] Other achieved properties include shape-reconfiguration, tunable nonlinear stiffness and dynamic characteristics, multistability, and impact absorption.Since the architected origami materials obtain their unique properties from the 3D geometries of the constituent sheets or modules, they can be considered a subset of architected cellular solids or mechanical metamaterials. [35][36][37][38][39] However, the origami materials have many unique characteristics. The rich geometries of origami offer us great freedom to tailor targeted Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geomet...

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Section: Folding Induced Mechanical Propertiesmentioning

confidence: 99%

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

et al. 2018

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“…More recently, generalizations of the Hertzian contact law have been explored in the context of mechanical metamaterials, including those with strainsoftening behavior (where 0 < p < 1) [31]. Examples of this include tensegrity structures [32] and origami metamaterial lattices [33,34]. Motivated by those recent works, we will examine the formation of dispersive shock waves for general values of p. We find a fundamentally different dynamical behavior for the two cases of p > 1 and p < 1.…”

Section: Introductionmentioning

confidence: 90%

“…Let u n be the relative displacement from equilibrium of the n-th particle in the lattice. As discussed in the introduction, we are motivated by the generalization of the Hertzian contact model to arbitrary powers not only due to applications [32][33][34], but also due to significant theoretical developments (e.g., regarding traveling waves) [24,36,37]. In that light, we consider the following equations of motion:…”

Section: Theoretical Analysismentioning

confidence: 99%

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

et al. 2017

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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.

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“…Recently, origami has emerged as a promising building block of mechanical metamaterials with versatile functionalities and programmability [7][8][9][10][11][12][13][14][15][16][17], due to its capability of transforming a 2D crease pattern into a complex 3D sculpture, purely geometric traits independent of both scale and constituent materials, and ease of manufacturing [18,19].…”

Section: Introductionmentioning

confidence: 99%

Folding of Tubular Waterbomb

Feng

Chen

et al. 2020

Research

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Origami has recently emerged as a promising building block of mechanical metamaterials because it offers a purely geometric design approach independent of scale and constituent material. The folding mechanics of origami-inspired metamaterials, i.e., whether the deformation involves only rotation of crease lines (rigid origami) or both crease rotation and facet distortion (nonrigid origami), is critical for fine-tuning their mechanical properties yet very difficult to determine for origami patterns with complex behaviors. Here, we characterize the folding of tubular waterbomb using a combined kinematic and structural analysis. We for the first time uncover that a waterbomb tube can undergo a mixed mode involving both rigid origami motion and nonrigid structural deformation, and the transition between them can lead to a substantial change in the stiffness. Furthermore, we derive theoretically the range of geometric parameters for the transition to occur, which paves the road to program the mechanical properties of the waterbomb pattern. We expect that such analysis and design approach will be applicable to more general origami patterns to create innovative programmable metamaterials, serving for a wide range of applications including aerospace systems, soft robotics, morphing structures, and medical devices.

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Formation of rarefaction waves in origami-based metamaterials

Cited by 67 publications

References 28 publications

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

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

Folding of Tubular Waterbomb

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