Solitary waves in a bistable lattice

Katz, Shmuel; Givli, Sefi

doi:10.1016/j.eml.2018.06.003

Cited by 62 publications

(21 citation statements)

References 32 publications

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“…This bistable response has been observed in some case studies at the macroscopic scale [40,41]. It can be expediently utilized to develop tunable, switchable and/or reconfigurable metamaterials, which are also able to support solitary wave dynamics [42].…”

Section: Introductionmentioning

confidence: 65%

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

2020

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A bistable response is an innate feature of tensegrity metamaterials, which is a conundrum to attain in other metamaterials, since it ushers unconventional static and dynamical mechanical behaviors. This paper investigates the design, modeling, fabrication and testing of bistable lattices with tensegrity architecture and nanoscale features. First, a method to design bistable lattices tessellating tensegrity units is formulated. The additive manufacturing of these structures is performed through multiphoton lithography, which enables the fabrication of microscale structures with nanoscale features and extremely high resolution. Different modular lattices, comprised of struts with 250 nm minimum radius, are tested under loading-unloading uniaxial compression nanoindentation tests. The compression tests confirmed the activation of the designed bistable twisting mechanism in the examined lattices, combined with a moderate viscoelastic response. The force-displacement plots of the 3D assemblies of bistable tensegrity prisms reveal a softening behavior during the loading from the primary stable configuration and a subsequent snapping event that drives the structure into a secondary stable configuration. The twisting mechanism that characterizes such a transition is preserved after unloading and during repeated loading-unloading cycles. The results of the present study elucidate that fabrication of multistable tensegrity lattices is highly feasible via multiphoton lithography and promulgates the fabrication of multi-cell tensegrity metamaterials with unprecedented static and dynamic responses.

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Section: Introductionmentioning

confidence: 65%

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

2020

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“…A second direction of research concerns the theoretical and numerical analysis of the model (3) for general (and not necessarily polynomial) expressions of Ericksen energy. In the case of a piecewise linear energy, it has been proven in [17] that solitary waves are generated, or on the contrary that stop-band behaviors are obtained, depending on the slopes of the energy.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of a regularized and bistable Ericksen bar using an extended Lagrangian approach

Bourgeois

Favrie

Lombard

2020

International Journal of Solids and Structures

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The motivation of this work is to better understand the dynamic behaviour of bistable structures presenting an analogy with reguralized Ericksen bars. The archetype of such structures is the bistable tape spring, which exhibits a particular scenario of deployment, from the stable coiled configuration to the straight stable configuration: at each time of the deployment, the geometry of the tape is similar to a two-phase bar with a coiled part and a straight part separated by a transition zone that moves along the tape. One goal of this work is to show that a reguralized and bistable Ericksen bar model contains all the properties to reproduce such a dynamic behaviour. The mathematical structure of this model presents a locally non-convex potential with two minima and a dependence of higher order terms. Some similarities exist between this model and the Euler-Korteweg system with a Van der Waals equation. To study numerically the dynamic behaviour of such models, it is necessary to solve a dispersive and conditionally hyperbolic system. For this purpose, the Lagrangian of the regularized bistable Ericksen model is extended and penalized. Variable boundary conditions are deduced from Hamilton's principle and are used to control the evolution of the system. Dispersion analysis allows to determine the numerical parameters of the model. The obtained non-homogeneous hyperbolic system can be solved by standard splitting strategy and finite-volume methods. Numerical simulations illustrate how the parameters of the model influence the width and the propagation speed of the transition zone. The effect of energy dissipation is also examined. Finally, comparisons with an exact kink wave solution indicate that the extended Lagrangian solution reproduces well the dynamics of the original Lagrangian.

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“…Another important dynamic property achievable in arrays of multistable elements is energy localization. Indeed, recent studies demonstrated the creation of propagating wave fronts along one-and two-dimensional arrays of bistable elements [7][8][9][10][11]. Finally, the ability to employ a single input to bring a configuration of discretely [12,13] and continuously [14] interconnected bistable elements from one stable equilibrium state to another, was achieved by embedding these locally bistable structures with viscous fluid.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of reconfigurable straw-like elements

Ilssar¹,

Pukshansky²,

Or³

et al. 2022

Preprint

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In this paper, we discuss the dynamic modeling of fluid-filled straw-like elements consisting of serially interconnected elastic frusta with both axisymmetric and antisymmetric degrees of freedom, assuming planar motion. Under appropriate conditions each sub-structure has four stable equilibrium states. This gives the system under investigation the ability to remain stable in a large number of complex states, which is a vital ability for myriad of applications, including reconfigurable structures and soft robots. The theoretical model explains the dynamics of a single straw-like element in a discrete manner, considering inertial, damping, and gravitational effects, while taking into account the nonlinear elasticity of the elastic frusta, and assuming hydrostatic behavior of the entrapped fluid. After identifying the geometric and elastic parameters of the theoretical model based on relatively simple experiments, the model is validated compared to numerical simulations and experiments. The numerical simulations validate the theoretical elasticity of the elastic frusta, whereas the overall dynamic behavior of the system and the influence of unmodeled fluidic effects are examined experimentally. It is demonstrated both theoretically and empirically that straw-like elements cannot be adequately modeled using simple uniaxial deformations. In addition, the experimental validation indicates that the suggested model can accurately capture their overall dynamics.

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Solitary waves in a bistable lattice

Cited by 62 publications

References 32 publications

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

Dynamics of a regularized and bistable Ericksen bar using an extended Lagrangian approach

Dynamics of reconfigurable straw-like elements

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