Large acoustoelastic effect

Abiza, Zaki; Destrade, Michel; Ogden, Ray W.

doi:10.1016/j.wavemoti.2011.12.002

Cited by 53 publications

(28 citation statements)

References 24 publications

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“…Landau and Lifshitz 42 write the strain energy W 3 up to third order by including terms in I 3 , I 1 I 2 , and I 3 1 . There are 4 combinations of the invariants in the strain energy at the fourth order: I 1 I 3 ; I 2 1 I 2 , I 2 2 , and I 4 1 , thus the fourth-order strain energy is 36,[43][44][45] …”

Section: Appendix: Fourth Order Elasticity Theorymentioning

confidence: 99%

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Gallot

Malcolm

Szabo

et al. 2015

Journal of Applied Physics

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The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility of using the nonlinear characterization of rocks as an imaging tool in the field. In our experiment, we study the nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump in a room-dry 15 Â 15 Â 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the strain in our sample, we also measured the particle velocity at the sample surface to scale a finite difference linear elastic simulation to estimate the complex strain field in the sample, on the order of 10 À6 , induced by the S-wave pump. We derived a fourth order elastic model to relate the changes in elasticity to the pump strain components. We recover quadratic and cubic nonlinear parameters:b ¼ À872 and d ¼ À1:1 Â 10 10 , respectively, at room-temperature and when particle motions of the pump and probe waves are aligned. Temperature fluctuations are correlated to changes in the recovered values ofb andd, and we find that the nonlinear parameter changes when the particle motions are orthogonal. No evidence of slow dynamics was seen in our measurements. The same experimental configuration, when applied to Lucite and aluminum, produced no measurable nonlinear effects. In summary, a method of selectively determining the local nonlinear characteristics of rock quantitatively has been demonstrated using traveling sound waves. V C 2015 AIP Publishing LLC.

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Section: Appendix: Fourth Order Elasticity Theorymentioning

confidence: 99%

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Gallot

Malcolm

Szabo

et al. 2015

Journal of Applied Physics

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“…Low-frequency wave propagation in solids is relevant to a large number of modern applications (see, for example, [1,2,3,4,5,6,7] and references therein). Long longitudinal bulk strain solitary waves in elastic waveguides can be modelled using Boussinesq-type equations [1,2,8] (see also [5,9,10,11,12]).…”

Section: Introductionmentioning

confidence: 99%

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Хуснутдинова

Tranter

2019

Advanced Structured Materials

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Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in which case the system can support radiating solitary waves. We construct a weakly-nonlinear d'Alembert-type solution of this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. Asymptotic validity of the solution is carefully examined numerically. We also discuss the limiting case of an infinite interval for localised initial conditions. The solution is applied to study interactions of radiating solitary waves.

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“…However, the initial stress σ ij must satisfy (σ ij σ ij )(c ijklmn c ijklmn ) << (c ijkl c ijkl ) 2 in the classic acoustoelastic theory, where c ijkl and c ijklmn are the second-order and third-order elastic constants (Johnson and Rasolofosaon, 1996). Because the third-order elastic constants are usually much greater than the second-order elastic constants, this means that the initial deformation induced by the initial stress applicable for the classic acoustoelastic theory must be infinitesimal, which has been verified in the relevant experiments (Abiza et al, 2012). Furthermore, the FSPM usually have complex nonlinear constitutive law, rather than the constitutive law of the third-order elastic constants in the classic acoustoelastic theory, especially at the large pre-deformation.…”

Section: Introductionmentioning

confidence: 77%

“…Furthermore, the FSPM usually have complex nonlinear constitutive law, rather than the constitutive law of the third-order elastic constants in the classic acoustoelastic theory, especially at the large pre-deformation. Although the higher-order elastic constants may be introduced into constitutive law, this will increase the difficulty greatly (Abiza et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Incremental algorithm for acoustoelastic theory of large static pre-deformed fluid-saturated porous media

Tian

Wang

2017

PCFD

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Abstract:The incremental acoustoelastic equations for fluid-saturated porous media (FSPM) under the large static pre-deformation are derived in this paper by incremental loading method based on classic acoustoelastic theory of FSPM, which provides quantitative acoustoelastic relation of FSPM with arbitrary constitutive equation. Isotropic FSPM with third-order constitutive equation are taken as an example to give the relation between wave velocity and confining pressure and discuss the effect of loading step on acoustoelastic relations of isotropic FSPM under closed-pore jacketed condition and opened-pore jacketed condition.

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Large acoustoelastic effect

Cited by 53 publications

References 24 publications

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Incremental algorithm for acoustoelastic theory of large static pre-deformed fluid-saturated porous media

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