Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

Kanaun, S. K.; Levin, V. M.; Sabina, Federico J.

doi:10.1016/j.wavemoti.2003.12.013

Cited by 58 publications

(44 citation statements)

References 22 publications

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“…They are almost identical at frequencies where k 1 a < 1 and are also very close to each other at high frequencies. This is quite contrary to the expectation [Kanaun et al 2004] that these two models would predict substantially different results in the wave speed and coherent attenuation since the matrix phase is treated quite differently in these two models, as a continuous phase in the EMT-2 as opposed to an equivalent inclusion in the EMT-1. Relatively large deviations are seen at the frequencies where the attenuation has a peak due to the rigid-body resonance of the inclusions (see Figures 2 and 3) and at some high frequencies where numerous elastic resonances occur (see Figure 4).…”

Section: Resultscontrasting

confidence: 77%

“…As shown in [Kim et al 1995], this theory was very successful in predicting the effective wave speed and attenuation in random particulate composites for wide ranges of frequency and volume fraction. A second variant is the dynamic extension [Sabina and Willis 1988;Bussink et al 1995;Kanaun and Levin 2003;Kanaun et al 2004] of the static self-consistent theories of [Budiansky 1965;Hill 1965]. The major difference between these two theories lies in how the roles of constituents are treated, which will be discussed later in this paper.…”

Section: Jin-yeon Kimmentioning

confidence: 99%

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Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

Kim

2010

J. Mech. Mater. Struct.

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Two effective medium models for two-dimensional scalar wave propagation in random inhomogeneous media are examined in a single theoretical framework. It is shown how the hypotheses and self-consistency conditions in these models are mathematically formulated. As a special case, a two-phase composite in which circular cylindrical inclusions are embedded in a continuous matrix is considered. Numerical calculations are performed for such composites with different combinations of constituent properties in the frequency range up to ka = 10, where geometric optic behavior starts appearing. The models mutually deviate when the motion of inclusions is relatively large, such as at the resonance scattering of the inclusions. Otherwise, deviations in the low-frequency regime (ka < 1) are negligible and those at high frequencies are also strikingly small. The same facts are observed for two composites having very different constituent properties and in the high-frequency limit.

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Section: Resultscontrasting

confidence: 77%

Section: Jin-yeon Kimmentioning

confidence: 99%

Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

Kim

2010

J. Mech. Mater. Struct.

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“…Accepted pattern consists of O node and E ± ij points, separated from the point O by distance λ ij τ . In the future discussion values of the functions at the point O are denoted by upper index "0", values at the points E ± ij are denoted by lower index "ij" and the upper index "±" (for example σ ± ij ), and values at point A are not not denoted by an additional index [13][14][15][16].…”

Section: The Defining Equations Of Bicharacteristicsmentioning

confidence: 99%

The Method and Software for the Solution of Dynamic Waves Propagation Problem in Elastic Medium

2016

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This paper describes the numerical method for the solution to the problem of propagation of dynamic waves in elastic media -the bicharacteristics method with the usage of the ideas of the splitting method. The bicharacteristics method is one of the most convenient methods for software creating. In this research paper we have worked on the solution for non-stationary problem of the homogeneous isotropic elastic body dynamics using the bicharacteristics method, based on which the "ProgWave" software was designed. With this software, we have obtained the plots of isolines of normal and tangent tensions, which are very important for the studies of non-stationary dynamic waves propagation in flat elastic bodies, in engineering practice at construction designs calculation, in problems of mechanical engineering, etc.

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“…One of the two basic patterns in self-consistent approach is effective medium. The fundamental hypothesis in the group of the effective medium methods explains that the composite material outside the abutting of the inclusion may be varied by the effective properties of the entire composite that is assumed a homogenous medium (Kanaun 2004). The next self-consistent method is the effective field method.…”

Section: Multiple Scattering Approachesmentioning

confidence: 99%

“…By using both the effective medium and effective field methods, Kanaun et al (2004) extracted the equations of elastic wave scattering in composites containing of spherical inclusions. They showed that the effective field method has some advantages than the effective medium.…”

Section: Introductionmentioning

confidence: 99%

Elastic wave propagation in nano-composites with random distribution of spherical inclusions

Rahimzadeh

2013

Lat. Am. j. solids struct.

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In the present study, efforts have been made to theoretically study the diffraction of plane harmonic compressional waves by a spherical nano-inclusion based on the Gurtin-Murdoch surface/interface elasticity theory in which the interface between the nano-inclusion and the matrix is considered as the material surface which has their own mechanical properties. Furthermore, a nano-composite has been considered in order to assess the size effect on the wave propagation characteristics of a plane compressional elastic wave containing the randomly distributed spherical nano-inclusions. Also, the phase velocities and attenuations of P and SV elastic waves along with the related dynamic effective elastic properties have been investigated for a wide variety of frequencies and volume fractions.

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Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

Cited by 58 publications

References 22 publications

Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

The Method and Software for the Solution of Dynamic Waves Propagation Problem in Elastic Medium

Elastic wave propagation in nano-composites with random distribution of spherical inclusions

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