Propagation and interaction of non-linear elastic plane waves in soft solids

Domanski, Wlodzimierz

doi:10.1016/j.ijnonlinmec.2008.12.006

Cited by 8 publications

(12 citation statements)

References 9 publications

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“…Domański [9,10] analyzed the third-order nonlinear effects and the interaction of plane waves in soft solids, respectively, based on the material model proposed by Hamilton et al [11]. Porubov and Maugin [12] applied nonlinear strain waves to study the growth of long bones.…”

Section: Introductionmentioning

confidence: 99%

Adjustable solitary waves in electroactive rods

Wang

Zhang

Dai

et al. 2015

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 99%

Adjustable solitary waves in electroactive rods

Wang

Zhang

Dai

et al. 2015

Journal of Sound and Vibration

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“…where E is the Green strain tensor and µ, A, and D are second, third-, and fourth-order elasticity constants, respectively, at least 16 articles [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have studied the dynamics of those solids.…”

Section: Introductionmentioning

confidence: 99%

Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect

Destrade

Gilchrist

Saccomandi

2010

The Journal of the Acoustical Society of America

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Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρv 2 , where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρv 2 = a + be + ce 2 , say, a depends linearly on µ; b on µ and A; and c on µ, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.

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“…In this case we obtain that 1 + 1 2 = 0 and that 2 = 2 1 = 0 (see [6] or [2] for details). Therefore, we can formulate the following lemma.…”

Section: Threefold Axismentioning

confidence: 82%

“…Our aim in this work is to derive equations similar to those in [2] but by a different method. Here, unlike the presentation in [2] (see also [3][4][5][6][7][8]), where the method of weakly nonlinear geometric optics was used, we will apply a double-scale expansion. Instead of introducing a new fast variable and applying geometric optics-type asymptotics, which leads to evolution equations with three independent variables, we introduce here just two new independent variables: a slow time variable τ and a characteristic variable θ .…”

Section: Introductionmentioning

confidence: 99%

The complex Burgers equation as a model for collinear interactions of weakly nonlinear shear plane waves in anisotropic elastic materials

Domanski

2014

J Eng Math

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Collinear interactions of weakly nonlinear quasi-shear plane waves in anisotropic (in particular fiberreinforced) compressible elastic materials are analyzed. Evolution equations for quasi-shear wave amplitudes are derived with the help of the asymptotic method of a double-scale expansion. It is shown that quadratically nonlinear coupling is possible when shear waves propagate along a special fiber direction in anisotropic materials. The evolution equations are reduced to a single inviscid complex Burgers equation when the fiber direction is a threefold symmetry acoustic axis. Some properties of this equation are analyzed. General considerations are illustrated on examples of shear waves propagating along a threefold symmetry acoustic axis in a cubic crystal and in an icosahedral quasicrystal.

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Propagation and interaction of non-linear elastic plane waves in soft solids

Cited by 8 publications

References 9 publications

Adjustable solitary waves in electroactive rods

Adjustable solitary waves in electroactive rods

Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect

The complex Burgers equation as a model for collinear interactions of weakly nonlinear shear plane waves in anisotropic elastic materials

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