Observation of vector solitary waves in soft laminates using a finite-volume method

Ziv, Ron; Gal, Shmuel

doi:10.1016/j.ijnonlinmec.2020.103502

Cited by 6 publications

(2 citation statements)

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“…The growth and decay of discontinuities might be further investigated using dedicated techniques [14,36]. Future works could also encompass the study of travelling waves [37], steady shocks [14], and solitary waves in layered media [38]. Results could be extended to pre-strained solids [31], other viscoelastic material models [39], poroelasticity [27], and poro-viscoelasticity [26,40].…”

Section: Discussionmentioning

confidence: 99%

“…The maximum value Ω 1 /Ω v of the dissipation factor is reached at the characteristic frequency ω = Ω v given by Ω v = 1 − g /τ, and Ω 1 = g /(2τ) is the decay rate of viscoelastic acceleration waves (20). Partial Fourier transformation of the equations of motion in time domain yields the harmonic oscillator equation ∂ 2 Y v + κ 2 v = 0 for the velocity field, where the wavenumber κ is a root of the quadratic equation (38) to be specified. Integration of the differential equation for v with v| Y =0 = V gives v = V e −iκY + θ sin(κY ) where θ is arbitrary.…”

Section: A Linear Solutionmentioning

confidence: 99%

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Shear shock formation in incompressible viscoelastic solids

Berjamin,

Senthilnathan

2021

Preprint

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Experiments have shown that shear waves induced in brain tissue can develop into shock waves, thus providing a possible explanation of deep traumatic brain injuries. Here, we study the formation of shock waves in soft viscoelastic solids subject to an imposed velocity at their boundary. We consider the plane shearing motion of a semi-infinite half-space, which corresponds to a spatially one-dimensional problem. Incompressible soft solids whose behaviour is described by the Fung-Simo quasi-linear viscoelasticy theory (QLV) are considered, where the elastic response is either exponential or polynomial of Mooney-Rivlin-Yeoh type. Waveform breaking can occur at the blow-up of acceleration waves, leading to one sufficient condition for the formation of shocks. A slow scale analysis based on a small amplitude parameter yields a damped Burgers-like equation, thus leading to another shock formation condition. Numerical experiments performed using a dedicated finite volume scheme show that these estimates have limited accuracy. Their validity is restricted in the elastic limit too, where exact shock formation conditions are known.

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