Universal energy transport law for dissipative and diffusive phase transitions

Nadkarni, Neel; Daraio, Chiara; Abeyaratne, Rohan; Kochmann, Dennis M.

doi:10.1103/physrevb.93.104109

Cited by 38 publications

(37 citation statements)

References 29 publications

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“…We recently reported a universal scaling law for the energy transported by 1D transition waves in periodic networks of bistable elements [9]. As shown in the following, those results also apply to planar transition fronts propagating in the 2D discrete system discussed here with important implications on width, speed, and energy of moving domain walls.…”

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

confidence: 57%

“…The dissipative/diffusive nature of the system ensures that, far from the interface region (i.e., for |z| → ∞) the polarization ϕ assumes a constant, steady value (ϕ + or ϕ − ) so that ϕ(z +ê · ∆x γ ) − ϕ(z) → 0. This can be shown to make the interaction term vanish [9]. In addition, a similar argument can be applied to the inertial term.…”

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

confidence: 91%

“…which can easily be obtained by scaling arguments of the total kinetic and potential energy and the total dissipation potential [9]. Insertion into (S15) along with (S17) for centro-symmetric lattices shows that all terms of order O(a 3 ) and higher vanish in the continuum limit (i.e., as a → 0).…”

Section: Discrete Network and Continuum Limitmentioning

confidence: 91%

“…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). We note that the above scaling law applies even in the limit ρ → 0 [9]. Let the 1D variation of the polarization perpendicular to an Ising-type domain wall be approximated by…”

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

confidence: 99%

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

confidence: 57%

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

confidence: 91%

Section: Discrete Network and Continuum Limitmentioning

confidence: 91%

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

confidence: 99%

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Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Frazier

Kochmann

2017

Advanced Materials

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“…For a detailed discussion of the continuum limit and the energetic requirements for stable wave propagation, see ref. 35. The linear damping model is a leading-order approximation to the complex dissipative nature of elastomers.…”

Section: Numerical Resultsmentioning

confidence: 99%

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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Emerging Themes and Future Directions

2017

Harnessing Bistable Structural Dynamics

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Universal energy transport law for dissipative and diffusive phase transitions

Cited by 38 publications

References 29 publications

Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

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

Emerging Themes and Future Directions

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