Evidence of microstructure evolution in solid elastic media based on a power law analysis

Scalerandi, Marco; Idjimarene, Sonia; Bentahar, Mourad; Guerjouma, Rachid El

doi:10.1016/j.cnsns.2014.09.007

Cited by 26 publications

(10 citation statements)

References 52 publications

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“…Finally, power law relations best describe the strain dependence [ Scalerandi et al , ; Bruno et al , ; Rivière et al , ], as observed in Figure c:

{(|, \frac{Δc}{c})}_{nf} = Φ_{3} ε^{ν},

or equivalently

\log ((), {(|, \frac{Δc}{c})}_{nf}) = ν \log ((), ε) + \log (Φ_{3}),

…”

Section: Resultsmentioning

confidence: 99%

“…where P 0 represents a characteristic pressure, which might differ for the different harmonics. Applying a log transformation to this equation yields to the following linear relation: Finally, power law relations best describe the strain dependence [Scalerandi et al, 2015;Bruno et al, 2009;Rivière et al, 2015], as observed in Figure 3c:…”

Section: 1002/2016gl068061mentioning

confidence: 97%

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Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

Rivière

Pimienta

Scuderi

et al. 2016

Geophysical Research Letters

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Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi‐static ( f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.

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“…Finally, power law relations best describe the strain dependence [ Scalerandi et al , ; Bruno et al , ; Rivière et al , ], as observed in Figure c:

{(|, \frac{Δc}{c})}_{nf} = Φ_{3} ε^{ν},

or equivalently

\log ((), {(|, \frac{Δc}{c})}_{nf}) = ν \log ((), ε) + \log (Φ_{3}),

…”

Section: Resultsmentioning

confidence: 99%

Section: 1002/2016gl068061mentioning

confidence: 97%

Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

Rivière

Pimienta

Scuderi

et al. 2016

Geophysical Research Letters

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“…On using the fitting function log(−( Δ c / c ) 0 ω ) = ν log( ϵ 1 ω )+ log( a ) we find a , the amplitude of the offset and ν which tells us how on average the offset scales with strain. As pointed out in previous studies [ Xu et al , ; Van Den Abeele et al , ; Scalerandi et al , ], analyzing ν values among samples can help classify different nonlinear mechanisms, while a values tell us how much of a mechanism is present in each sample. For instance, it has been reported that the exponent ν increases from 1 up to 3 with mechanical or thermal loadings in concrete, as the damage properties evolve from intrinsic damage (closed cracks, grain‐grain contacts, dislocations,...) to macrodamage (open cracks) Scalerandi et al [].…”

Section: Resultsmentioning

confidence: 99%

A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

et al. 2015

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Key Points:• We perform a systematic classification of nonlinear elastic behavior in rocks • Two physical mechanisms can describe the nonlinear elasticity of these rocks Abstract Dynamic acoustoelastic testing is performed on a set of six rock samples (four sandstones, one soapstone, and one granite). From these studies at 20 strain levels 10 −7 < <10 −5 , four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy and a fifth measure of nonlinear elastic response is found. These five measures of the nonlinear elastic response of the samples (approximately 3 × 6 × 20 × 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis using model-independent statistical methods, principal component analysis, and fuzzy clustering. This analysis reveals differences among the samples and differences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fifth is seeing something different. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples, there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classification of the samples into two groups. The numbers in this study and the classification of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.

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“…Finally, we recall that most commonly the nonlinearity of a sample is classified according to a power-law dependence of the nonlinear indicator on a not univocally specified "amplitude" of excitation [20,21], which often is the strain amplitude evaluated at the same spatial position where the signal is measured. Different components of the strain field are neglected and often the longitudinal component only (to which the detecting sensor is more sensible) is considered, which is correct when one-dimensional (1D) geometries are considered.…”

Section: Introductionmentioning

confidence: 99%

Separation of Damping and Velocity Strain Dependencies using an Ultrasonic Monochromatic Excitation

2019

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Precise knowledge of the dependence of elastic modulus and Q factor on the amplitude of excitation is a prerequisite for the development and validation of models to explain the hysteresis observed in quasistatic experiments for various media, i.e., the different deformations at the same applied stress observed when stress change rate is positive or negative. Separation of different contributions to dynamic nonlinearity (e.g., those due to nonequilibrium effects, often termed conditioning) and independent estimation of nonlinearities originated by the strain dependence of velocity and the damping factor are required, which is often not possible with standard approaches. Here we propose and validate a method that, measuring the response of a sample to a monochromatic excitation at different amplitudes, allows fast, continuous, and quasi-real-time monitoring of the dependence of the material elastic properties on amplitude: dynamic elastic modulus (related with velocity through density) and Q factor of the mechanical resonances (related with wave-amplitude attenuation parameters).

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Evidence of microstructure evolution in solid elastic media based on a power law analysis

Cited by 26 publications

References 52 publications

Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

Separation of Damping and Velocity Strain Dependencies using an Ultrasonic Monochromatic Excitation

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