Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods

Wang, Y. Z.; Dai, Hui–Hui; Chen, W. Q.

doi:10.1063/1.4929721

Cited by 10 publications

(3 citation statements)

References 42 publications

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“…Hence it is not appropriate to describe the dissipative stress in the solid usingĖ left . Recent studies [24,30] have also emphasized that the strain-rate tensor is not appropriate for incorporating viscous dissipative effects, as it yields unphysical results in the context of wave formation in prestressed viscoelastic solids [31]. In this work, we employ both formulations and demonstrate how the use of the (incorrect) strain-rate formulation for the dissipative stress leads to results that are drastically different from the rate-of-deformation formulation.…”

Section: Problem Formulationmentioning

confidence: 96%

Consistent formulation of solid dissipative effects in stability analysis of flow past a deformable solid

Giribabu

Shankar

2016

Phys. Rev. Fluids

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The linear stability of plane Couette flow past a deformable solid is analyzed in the creeping-flow limit with an objective towards elucidating the consequences of employing two widely different formulations for the dissipative stresses in the deformable solid. One of the formulations postulates that the dissipative stress is proportional to the strain-rate tensor based on the left Cauchy-Green tensor, while in the other the dissipative stress in the solid is proportional to the rate-of-deformation tensor. However, it is well known in continuum mechanics that the rate-of-deformation tensor obeys the fundamental principle of material-frame indifference while the strain-rate-tensor formulation does not and hence it is more appropriate to employ the rate-of-deformation tensor in the description of dissipative stresses in deformable solids. In this work we consider the specific context of stability of plane Couette flow past a deformable solid and demonstrate that the results concerning the stability of the system from both models differ drastically. In the rate-of-deformation formulation for the dissipative stress, there is a range of solid-fluid thickness ratios (between 1.21 and 1.46) wherein the system is always stable for nonzero values of solid viscosity, unlike the strain-rate-tensor formulation wherein the system is unstable at all values of solid thickness. Further, for a solid-fluid thickness ratio less than 1, incorporation of dissipative effects in the solid using the rate-of-deformation formulation shows that the flow is more unstable compared to a purely elastic neo-Hookean solid, while for strain-rate-tensor formulation the flow is stabilized with an increase in viscosity of the solid. Using the fundamentally correct dissipative stress formulation, we also address the stability of pressure-driven flow in a deformable channel, wherein previous work carried out for an elastic neo-Hookean solid has shown that only the shortwave instability (driven by the first normal stress difference in the solid) exists while the finite-wave instability is absent in the creeping-flow limit. Using a consistent formulation for viscous stresses in the solid, we show that the shortwave instability is completely stabilized beyond a critical viscosity of the solid. Thus the present study clearly demonstrates the importance of consistent modeling of dissipative effects in the solid in order to accurately predict the stability of fluid flow past deformable solid surfaces.

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Section: Problem Formulationmentioning

confidence: 96%

Consistent formulation of solid dissipative effects in stability analysis of flow past a deformable solid

Giribabu

Shankar

2016

Phys. Rev. Fluids

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“…Moreover, the excitations of different nonlinear waves can be tuned by changing the axial pre-stretch. Furthermore, the kink and kink-like waves propagating in pre-stretched Mooney-Rivlin viscoelastic rods were investigated by Wang et al [105]. The numerical examples indicated that the pre-stretch and viscosity influence the wave shape and nonlinear wave velocity.…”

Section: Nonlinear Wavesmentioning

confidence: 99%

Vibrations and waves in soft dielectric elastomer structures

Zhao

Chen²,

Hu³

et al. 2023

International Journal of Mechanical Sciences

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“…Inspired by the earlier works mentioned above, we have conducted a systematic investigation in recent years on wave propagation in soft materials and structures in various configurations [17,18,[37][38][39][40][41][42]. In this paper, we intend to show that the combination of large deformation and electromechanical coupling can lead to a very flexible and efficient way to tune the BGs by considering a simple phononic cylinder of soft electroactive elastomer with periodic electric boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Tuning Elastic Waves in Soft Phononic Crystal Cylinders Via Large Deformation and Electromechanical Coupling

Zhou

Bao

et al. 2018

Journal of Applied Mechanics

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Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence, they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal (PC) cylinder made of dielectric elastomer (DE) to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes, which are mechanically negligible, are placed periodically along the DE cylinder, and hence, the material can be regarded as uniform in the undeformed state. This is also the case for the uniformly prestretched state induced by a static axial force only. The effective periodicity of the structure is then achieved through two loading paths, i.e., by maintaining the longitudinal stretch and applying an electric voltage over any two neighboring electrodes or by holding the axial force and applying the voltage. All physical field variables for both configurations can be determined exactly based on the nonlinear theory of electroelasticity. An infinitesimal wave motion is further superimposed on the predeformed configurations, and the corresponding dispersion equations are derived analytically by invoking the linearized theory for incremental motions. Numerical examples are finally considered to show the tunability of wave propagation behavior in the soft PC cylinder. The outstanding performance regarding the band gap (BG) property of the proposed soft dielectric PC is clearly demonstrated by comparing with the conventional design adopting the hard piezoelectric material. One particular point that should be emphasized is that soft dielectric PCs are susceptible to various kinds of failure (buckling, electromechanical instability (EMI), electric breakdown (EB), etc.), imposing corresponding limits on the external stimuli. This has been carefully examined for the present soft PC cylinder such that the applied electric voltage is always assumed to be less than the critical voltage except for one case, in which we illustrate that the snap-through instability of the axially free PC cylinder made of a generalized Gent material may be used to efficiently trigger a sharp transition in the BGs.

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Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods

Cited by 10 publications

References 42 publications

Consistent formulation of solid dissipative effects in stability analysis of flow past a deformable solid

Consistent formulation of solid dissipative effects in stability analysis of flow past a deformable solid

Vibrations and waves in soft dielectric elastomer structures

Tuning Elastic Waves in Soft Phononic Crystal Cylinders Via Large Deformation and Electromechanical Coupling

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