Nonlinear Acoustic Waves in Micro‐inhomogeneous Solids

Назаров, В. Е.; Радостин, А. В.

doi:10.1002/9781118698334

Cited by 19 publications

(30 citation statements)

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“…Furthermore, those rheological models clearly demonstrate that relaxation properties of the soft defects in addition to the elastic non-linearity (i.e. tensosensitivity of elastic moduli) inevitably lead to pronounced tensosensitivity of dissipation in microstructured solids (Zaitsev and Matveev, 2006;Zaitsev et al, 2008;Nazarov and Radostin, 2015) that may exhibit itself as dissipative non-linearity (which agrees with 544 V. Y. Zaitsev et al: Extracting real-crack properties from non-linear elastic behaviour of rocks considerations based on physical crack models Fillinger et al, 2006;Zaitsev et al, 2011;Zaitsev and Matveev, 2012).…”

Section: Introductionmentioning

confidence: 99%

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

Zaitsev

Радостин

Pasternak

et al. 2017

Nonlin. Processes Geophys.

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Abstract. Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P-and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance ( ∼ 80 %) of cracks with the normal-toshear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 %) portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.

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Section: Introductionmentioning

confidence: 99%

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

Zaitsev

Радостин

Pasternak

et al. 2017

Nonlin. Processes Geophys.

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“…Измерения эффектов АЗВТ показывают, что при относительно небольших амплиту-дах ε m , когда γ 0 ε n−1 m 1 и насыщения нелинейных потерь нет, для многих поликристал-лических металлов (например, медь [7], цинк [11,12]) и горных пород (гранит, магнезит, известняк [21,22]) показатель степени гистерезиса n = 2. Однако для этих материалов разные эффекты АЗВТ -декремент затухания и дефект модуля упругости -определя-ются разными параметрами нелинейности, и, следовательно, при n = 2 гистерезисная пет-ля σ = σ(ε, signε) состоит из двух квадратичных несимметричных параболических ветвей.…”

Section: в е назаров с б кияшкоunclassified

Saw-tooth waves in hysteretic media with a saturation of nonlinear losses

Назаров¹,

Kiyashko²

2015

Nelin. Dinam.

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На основе анализа результатов экспериментальных исследований эффектов амплитуд-но-зависимого внутреннего трения предложено гистерезисное (неупругого вида) уравнение состояния поликристаллических твердых тел с насыщением нелинейных потерь. Проведе-но теоретическое исследование распространения несимметричных пилообразных волн в та-ких материалах. Определены закономерности для характеристик нелинейной пилообразной волны: амплитудно-зависимых потерь и изменения скорости распространения волны, а так-же для амплитуд ее высших гармоник. Проведен графический анализ эволюции формы волны и ее спектральных составляющих.Ключевые слова: гистерезис, амплитудно-зависимое внутреннее трение, насыщение нелинейных потерь, пилообразные волны Экспериментальные исследования амплитудно-зависимого внутреннего трения (АЗВТ) в поликристаллических твердых телах свидетельствуют о том, что их уравнения состо-яния описываются гистерезисной зависимостью σ = σ(ε, signε), где σ и ε -напряже-ние и деформация [1-6], при этом во многих металлах (медь [4,7], алюминий [8], ин-дий [9, 10], цинк [11,12]

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“…Since recently, acoustics has been paying increasing attention to the study of nonlinear wave processes in micro-inhomogeneous solids [5][6][7]. The acoustic nonlinearity of such media is anomalously high in comparison with weakly nonlinear homogeneous media that are described by five-constant elasticity theory [3].…”

Section: Introductionmentioning

confidence: 99%

“…The equations of state for micro-inhomogeneous solids are often described by a nonanalytic continuous (but nonsmooth and nondifferentiable) function. The patterns of propagation and evolution of elastic waves in media with nonanalytic and quadratic (analytical) nonlinearities [1][2][3][4] differ qualitatively [7] from each other. This feature can be used for diagnostics and nondestructive testing of micro-inhomogeneous media.…”

Section: Introductionmentioning

confidence: 99%

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Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity

Назаров¹,

Kiyashko²

2018

Nelin. Dinam.

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On the basis of the elastic contact model of rough surfaces of solids, a quadraticallybimodular equation of state for micro-inhomogeneous media containing cracks is derived. A study is made of the propagation of elastic single unipolar pulse perturbations and bipolar periodic waves in such media. Exact analytical solutions that describe the evolution of initially triangular pulses and periodic sawtooth waves are obtained. A numerical and graphical analysis of the solutions is also carried out.

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Nonlinear Acoustic Waves in Micro‐inhomogeneous Solids

Cited by 19 publications

References 0 publications

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

Saw-tooth waves in hysteretic media with a saturation of nonlinear losses

Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity

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