Unidirectional Transition Waves in Bistable Lattices

Nadkarni, Neel; Arrieta, Andres F.; Chong, Christopher; Kochmann, Dennis M.; Daraio, Chiara

doi:10.1103/physrevlett.116.244501

Cited by 161 publications

(127 citation statements)

References 37 publications

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“…The propagation of rarefaction pulses is a rare find and thus a noteworthy feature of this system. Although compressive nonlinear solitary waves have been observed in nonlinear periodic systems as in, e.g., Hertzian contact-based chains (12,32,33) as well as in macroscopic nonlinear chains using magnetic connectors (19,34), rarefaction pulses have not been found in those, due to the lack of stiffness in tension, among other reasons. Finally, we note that the transition wave can also be initiated at any intermediate location along the chain, in which case a compressive pulse travels in one direction and a rarefaction pulse travels in the other direction, both propagating outward from the point of initiation (Movie S3).…”

Section: Resultsmentioning

confidence: 99%

“…1C, corresponding to the top image in Fig. 1D), displacing an element even to large amplitudes does not lead to a transition wave due to the energetically unfavorable (energy-absorbing) transition of each element (19). Therefore, because small-amplitude linear modes also disintegrate because of dissipation ( Fig.…”

Section: Response Under Large-amplitude Excitationsmentioning

confidence: 99%

“…The damping intrinsic to the soft materials removes all signals except the desired transition wave, which therefore propagates with high fidelity, predictability, and controllability. Furthermore, as observed for nondissipative (18) or minimally dissipative systems (19) made from stiff materials, a series of interacting bistable units can transmit nondispersive transition waves. By contrast, the proposed architecture is capable of propagating stable waves with constant velocity over arbitrary distances, overcoming both dissipative and dispersive effects, despite the soft, dissipative material of which it is composed.…”

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confidence: 99%

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Stable propagation of mechanical signals in soft media using stored elastic energy

Raney

Nadkarni

Daraio

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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308

199

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Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals.Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.soft | mechanical signal | stable propagation | instability S oft, highly deformable materials have enabled the design of new classes of tunable and responsive systems and devices, including bioinspired soft robots (1, 2), self-regulating microfluidics (3), adaptive optics (4), reusable energy-absorbing systems (5, 6), structures with highly programmable responses (7), and morphological computing paradigms (8). However, their highly deformable and dissipative nature also poses unique challenges. Although it has been demonstrated that the nonlinear response of soft structures can be exploited to design machines capable of performing surprisingly sophisticated functions on actuation (1, 2, 9), their high intrinsic dissipation has prevented the design of completely soft machines. Sensing and control functionalities, which require transmission of a signal over a distance, still typically rely on the integration of stiff electronic components within the soft material (10, 11), introducing interfaces that are often a source of mechanical failure.The design of soft control and sensing systems (and, consequently, completely soft machines) requires the ability to propagate a stable signal without distortion through soft media. There are two limiting factors intrinsic to materials that work against this: dispersion (signal distortion due to frequency-dependent phase velocity) and dissipation (loss of energy over time as the wave propagates through the medium). Dispersion can be controlled or eliminated through nonlinear effects produced via the control of structure in the medium (12). For example, periodic systems based on Hertzian contact (13-15), tensegrity structures (16), rigid bars and linkages (17), and bistable elastic elements (18) can behave as nondispersive media, with the nonlinearity of their local mechanical response canceling out the tendency for the signal to disperse at sufficiently large amplitudes. However, dissipation is still an ov...

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Section: Resultsmentioning

confidence: 99%

Section: Response Under Large-amplitude Excitationsmentioning

confidence: 99%

mentioning

confidence: 99%

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Stable propagation of mechanical signals in soft media using stored elastic energy

Raney

Nadkarni

Daraio

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

308

199

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“…Of course, damping in the system can be arbitrarily complex, so the linear approximation chosen here is only a leading-order approximation which, however, worked excellently for our experimentally investigated 1D bistable networks [12,13]. Linear gradient flow is also the most common kinetic model used in phase field description [5,6,7].…”

Section: Discrete Network and Continuum Limitmentioning

confidence: 99%

“…experimentally at the structural level in periodic 1D chains of elastically-coupled snapping shells [12] and snapping beams [13]. Also, transition waves travel only in the direction of decreasing energy (v · ∆ψ ≥ 0 since E d > 0 by definition and η > 0 by the second law of thermodynamics).…”

Section: Energy Transport and Domain Wall Motion In The Discrete Networkmentioning

confidence: 99%

Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Frazier

Kochmann

2017

Advanced Materials

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A mechanical metamaterial, a simple, periodic mechanical structure, is reported, which reproduces the nonlinear dynamic behavior of materials undergoing phase transitions and domain switching at the structural level. Tunable multistability is exploited to produce switching and transition phenomena whose kinetics are governed by the same Allen–Cahn law commonly used to describe material‐level, structural‐transition processes. The reported purely elastic mechanical system displays several key features commonly found in atomic‐ or mesoscale physics of solids. The rotating‐mass network shows qualitatively analogous features as, e.g., ferroic ceramics or phase‐transforming solids, and the discrete governing equation is shown to approach the phase field equation commonly used to simulate the above processes. This offers untapped opportunities for reproducing material‐level, dissipative and diffusive kinetic phenomena at the structural level, which, in turn, invites experimental realization and paves the road for new active, intelligent, or phase‐transforming mechanical metamaterials bringing small‐scale processes to the macroscopically observable scale.

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Resilience to Impact by Extreme Energy Absorption in Lightweight Material Inclusions Constrained Near a Critical Point

et al. 2016

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This work investigates a model design for lightweight, architected material inclusions that cultivate significant impact energy dissipation in structures. The inclusions are sustained near a critical point where damping is theoretically increased without bound. Using the principle, a material architecture and constraint mechanism are studied that exemplify the theory. Guided by a computational model and analysis, numerous specimens are fabricated and experimentation verifies that engineered material inclusions constrained nearer to critical points most effectively suppress structural dynamics following impact, minimize transmitted impulsive force, and better promote structural integrity. The concepts articulated here may find broad application for reusable, resilient protective structures.

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Unidirectional Transition Waves in Bistable Lattices

Cited by 161 publications

References 37 publications

Stable propagation of mechanical signals in soft media using stored elastic energy

Stable propagation of mechanical signals in soft media using stored elastic energy

Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Resilience to Impact by Extreme Energy Absorption in Lightweight Material Inclusions Constrained Near a Critical Point

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