Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering

Kube, Christopher M.; Turner, Joseph A.

doi:10.1063/1.4914698

Cited by 22 publications

(14 citation statements)

References 18 publications

(39 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Sections III and IV we will see that the Voigt-average estimation always overestimates the quasi-static limit of the velocities of the coherent waves. This conclusion is in agreement with that given by other works [49][50].…”

Section: Fig 4 Summation Of Strongly Connected Diagramssupporting

confidence: 94%

“…Both Weaver's model and Stanke-Kino's model use the Voigt-average material as the homogeneous reference medium. Turner pointed out the Voigt-averaged velocities always overestimate the velocities that measured in experiments [49]. To remedy this discrepancy, he introduced a selfconsistent scheme to calculate the properties of the homogeneous reference medium, and incorporated these material properties into Weaver's model [50].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

He¹

2019

Preprint

View full text Add to dashboard Cite

Scattering of elastic waves in heterogeneous media has become one of the most important problems in the field of wave propagation due to its broad applications in seismology, natural resource exploration, ultrasonic nondestructive evaluation and biomedical ultrasound. Nevertheless, it is one of the most challenging problems because of the complicated medium inhomogeneity and the complexity of the elastodynamic equations. A widely accepted model for the propagation and scattering of elastic waves, which properly incorporates the multiple scattering phenomenon and the statistical information of the inhomogeneities is still missing. In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation under the first-order smoothing approximation. The model establishes an accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. Starting from the elastodynamic differential equations, a system of integral equation for the Green functions of the heterogeneous medium was developed by using Green’s functions of a homogeneous reference medium. After properly eliminating the singularity of the Green tensor and introducing a new set of renormalized field variables, the original integral equation is reformulated into a system of renormalized integral equations. Dyson’s equation and its first-order smoothing approximation, describing the ensemble averaged response of the heterogeneous system, are then derived with the aid of Feynman’s diagram technique. The dispersion equations for the longitudinal and transverse coherent waves are then obtained by applying Fourier transform to the Dyson equation. The exact solution to the dispersion equations are obtained numerically. To validate the new model, the results for weak-property-fluctuation materials are compared to the predictions given by an improved weak-fluctuation multiple scattering theory. It is shown that the new model is capable of giving a more robust and accurate prediction of the dispersion behavior of weak-property-fluctuation materials. Numerical results further show that the new model is still able to provide accurate results for strong-property-fluctuation materials while the weak-fluctuation model is completely failed. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth’s lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovičić discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.

show abstract

Section: Fig 4 Summation Of Strongly Connected Diagramssupporting

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

He¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In Sections III and IV we will see that the Voigt-average estimation always overestimates the quasistatic limit of the velocities of the coherent waves. This conclusion is in agreement with that given by other works [49][50].…”

Section: Feynman's Diagram Dyson's Equation and The First-order-ssupporting

confidence: 94%

Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications

He¹

2019

Proceedings of Meetings on Acoustics

View full text Add to dashboard Cite

Scattering of elastic waves in heterogeneous media has become one of the most important problems in the field of wave propagation due to its broad applications in seismology, natural resource exploration, ultrasonic nondestructive evaluation and biomedical ultrasound.Nevertheless, it is one of the most challenging problems because of the complicated medium inhomogeneity and the complexity of the elastodynamic equations. A widely accepted model for the propagation and scattering of elastic waves, which properly incorporates the multiple scattering phenomenon and the statistical information of the inhomogeneities is still missing. In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact soluti on to the dispersion equation under the first-order smoothing approximation. The model establishes an accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. Starting from the elastodynamic differential equations, a system of integral equation for the Green functions of the heterogeneous medium was developed by using Green's functions of a homogeneous reference medium. After properly eliminating the singularity of the Green tensor and introducing a new set of renormalized field variables, the original integral equation is reformulated into a system of renormalized integral equations. Dyson's equation and its first-order smoothing approximation, describing the ensemble averaged response of the heterogeneous system, are then derived with the aid of Feynman's diagram technique. The dispersion equations for the longitudinal and transverse coherent waves are then obtained by applying Fourier transform to the Dyson equation. The exact solution to the dispersion equations are obtained numerically. To validate the new model, the results for weak-property-fluctuation materials are compared to the predictions given by an improved weak-fluctuation multiple scattering theory. It is shown that the new model is capable of giving a more robust and accurate prediction of the dispersion behavior of weak-property-fluctuation materials.Numerical results further show that the new model is still able to provide accurate results for strong-property-fluctuation materials while the weak-fluctuation model is completely failed. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth's lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the domi...

show abstract

“…Even for the simple anisotropic sphere case, near-field wave interactions become quite complex as these multiple vibration modes, angles, and wave fronts interfere. Recent analytical approaches have focused on far field backscattering approximations [5,6,7] but understanding the complex near field influence of anisotropy on wave propagation is largely unexplored and well suited to finite element approaches.…”

Section: Introductionmentioning

confidence: 99%

Ultrasound finite element simulation sensitivity to anisotropic titanium microstructures

Freed¹,

Blackshire²,

Na³

2016

AIP Conference Proceedings

View full text Add to dashboard Cite

Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering

Cited by 22 publications

References 18 publications

Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications

Ultrasound finite element simulation sensitivity to anisotropic titanium microstructures

Contact Info

Product

Resources

About