Elastodynamic wave propagation in graded materials: Simulations, experiments, phenomena, and applications

Vollmann, J.; Profunser, Dieter M.; Bryner, J.; Dual, Jürg

doi:10.1016/j.ultras.2006.05.073

Cited by 20 publications

(9 citation statements)

References 9 publications

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“…The nonlinear regression of the data illustrated the presence of a linear increase between the measured shear wave speed and mechanical‐excitation frequencies, consistent with a Voigt model at high frequencies (36, 39). The speed of elastic shear wave propagation has been correlated to the viscoelasticity of tissues and artificial materials in a number of different studies (27, 54, 55). These results suggest that, in combination with inversion methods that appropriately account for representative constitutive behavior of cartilage (1), dynamic MRE lends itself useful to the characterization of viscoelasticity and, possibly, other material parameters of cartilage.…”

Section: Discussionmentioning

confidence: 99%

Characterization of the dynamic shear properties of hyaline cartilage using high‐frequency dynamic MR elastography

Lopez

Amrami

Manduca

et al. 2008

Magnetic Resonance in Med

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This work evaluated the feasibility of dynamic MR Elastography (MRE) to quantify structural changes in bovine hyaline cartilage induced by selective enzymatic degradation. The ability of the technique to quantify the frequency-dependent response of normal cartilage to shear in the kilohertz range was also explored. Bovine cartilage plugs of 8 mm in diameter were used for this study. The shear stiffness ( s ) of each cartilage plug was measured before and after 16 hr of enzymatic treatments by dynamic MRE at 5000 Hz of shear excitation. Collagenase and trypsin were used to selectively affect the collagen and proteoglycans contents of the matrix. Additionally, normal cartilage plugs were tested by dynamic MRE at shear-excitations of 3000 -7000 Hz. Measured s of cartilage plugs showed a significant decrease (؊37%, P < 0.05) after collagenase treatment and a significant decrease (؊28%, P < 0.05) after trypsin treatment. Furthermore, a near-linear increase (R 2 ‫؍‬ 0.9141) in the speed of shear wave propagation with shear-excitation frequency was observed in cartilage, indicating that wave speed is dominated by viscoelastic effects. These experiments suggest that dynamic MRE can provide a sensitive quantitative tool to characterize the degradation process and viscoelastic behavior of cartilage. Magn Reson Med 59:356 -364, 2008.

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Section: Discussionmentioning

confidence: 99%

Characterization of the dynamic shear properties of hyaline cartilage using high‐frequency dynamic MR elastography

Lopez

Amrami

Manduca

et al. 2008

Magnetic Resonance in Med

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“…In Vollmann et al [7], a frequency-dependent wave propagation is pointed out in FGM when the material transition layer thickness amounts the same order of magnitude as the mechanical wave length. In the following the relationship of an incident pulse frequency spectrum to its propagation at the graded interface is discussed shortly.…”

Section: Resultsmentioning

confidence: 98%

“…As shown in Vollmann et. al [6] and Vollmann [7], when the material transition layer thickness amounts the same order of magnitude as the mechanical wave length, the wave scattering behavior at the interface becomes frequency dependent. The effect is of growing importance for micro-and nanostructures since the relative size of the interface layers is generally larger than in macroscopic structures.…”

Section: Introductionmentioning

confidence: 98%

P2F-4 Frequency Selective Wave Propagation in Graded Materials

Aebi

Loeffel

Bryner

et al. 2007

2007 IEEE Ultrasonics Symposium Proceedings

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Let's consider a mechanical stress pulse propagating in an elastic medium. When this pulse encounters a material or phase interface, which generally represents a change of the acoustic impedance, the pulse is split up into two parts. The first part is propagating further into the new material and the second part is reflected. The amplitude ratio of the reflected and the transmitted part is governed by the normalized difference of the acoustic impedance only, provided that the impedance change is a pure step function in space. If the acoustic impedance change is broadened spatially, the ratio of the transmitted and reflected part becomes frequency dependent and the effect can therefore be used for filtering, damping, acoustic isolation, and/or spectrum analysis purposes or for quantitative analysis of interfaces. The effect is of growing importance for micro-and nanostructures since the relative size of the interface layers is generally larger than in macroscopic structures.In this work, a pulse propagating in a linear elastic graded material is investigated with one-dimensional simulations. The numerical scheme is based on the Finite-Difference Time-Domain method (FDTD).The validation of the numerical model is carried out by comparing the simulated pulse propagation stress history with an analytical solution based on Chiu et al. [1].

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“…The disadvantages of the hybrid technique are: (a) it is difficult to derive fundamental solutions that are at the base of BIE, in some cases: coupled problems, geometrically or physically non-linear problems, inhomogeneous (functionally graded materials, see Vollmann et al (2006)) elastodynamics; (b) numerical integrations are time consuming; (c) great attention has to be paid to singular integrals; (d) the matrix of the resulting algebraic system is dense, fully populated and non-symmetric; (e) as mentioned above, a validation study has to be done for each new seismic scenario.…”

Section: Pros and Cons Of The Hybrid Msm-biemmentioning

confidence: 99%

Earthquakes site effects modeling by hybrid MS-BIEM: the case study of Sofia, Bulgaria

Panza

Paskaleva

Dineva

et al. 2009

Rend. Fis. Acc. Lincei

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The study solves 2D elastodynamic model for seismic in-plane wave propagation in laterally inhomogeneous geological profiles situated in a vertically inhomogeneous half-space with a seismic source. For the aim, an efficient hybrid Modal SummationBoundary Integral Equation Method (MSM-BIEM) is applied. The MSM is used as a tool for the simulation of wave propagation from the source position to the local multilayered laterally inhomogeneous geological profile, where the BIEM is applied. The BIEM is based on the frequency-dependent fundamental solution of the governing equation in elastodynamics and the hybrid method works in the frequency domain. The inverse FFT solution is applied to obtain time histories. The hybrid tool is applied to several models for the investigation of local site effects due to: (a) the impedance contrasts between soil layers, (b) surface topography and lateral inhomogeneity, (c) the seismic source properties and (d) the existence of water saturation in soils. The application of the modeling tool is a contribution to the seismic risk analysis of Sofia city. Abbreviations RMRay methods FDM Finite difference method MSM Modal summation method BIEM Boundary integral equation method DBIEM Direct boundary integral equation method MS-BIEM Modal summation-boundary integral equation method FFT Fast Fourier transform CPV integrals Cauchy Principal Value integrals List of symbolsVertically inhomogeneous half-space modeled with a series of M homogeneous flat layers C i , parallel to the free surfaceCommon boundary between X and X 0 q k , k k , l k Density and lame constants of each kth layer in X 0 a k , b k Complex longitudinal and shear wave velocities of each anelastic kth layer in X 0 V Pk , V Sk Real part of complex longitudinal and shear wave velocities of each anelastic kth layer in X 0

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Elastodynamic wave propagation in graded materials: Simulations, experiments, phenomena, and applications

Cited by 20 publications

References 9 publications

Characterization of the dynamic shear properties of hyaline cartilage using high‐frequency dynamic MR elastography

Characterization of the dynamic shear properties of hyaline cartilage using high‐frequency dynamic MR elastography

P2F-4 Frequency Selective Wave Propagation in Graded Materials

Earthquakes site effects modeling by hybrid MS-BIEM: the case study of Sofia, Bulgaria

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