Abstract The propagation of longitudinal and shear elastic waves through a multi-phase material was studied and the effective elastic properties of the medium were evaluated. The distribution of the reinforcing inclusions was considered random throughout the matrix. The effective dynamic properties of the composites, including their effective bulk and shear moduli and effective densities, were examined along with the effective phase velocity and attenuation of the incident P and S waves. The Sabina–Willis model was employed to study the wave propagation behavior, and the model performance was analyzed through comparison with experimental data from the literature. The results indicated that wave propagation significantly depended on the physical and mechanical properties of inclusions relative to those of the matrix and the normalized wave number of the propagated elastic wave. Moreover, despite the fact that the elastic properties of the incidence in the P and S waves exhibited a similar trend, their values differed significantly. The results can serve as a design criterion for composite materials under dynamic loading.

This paper aims to conduct a comparative study on four different models of effective field and effective medium for modeling propagation of plane elastic waves through the composites containing spherical particles with random distribution. Effective elastic properties along with the normalized phase velocity and attenuation of the average wave was numerically evaluated by the models. The plane incident wave was considered longitudinal to get the results. The numerical analyses were performed on four types of composites in the range of low to intermediate frequency and different volume fractions. Judgment about this comparative study is done based on physical and theoretical concepts in the wave propagation phenomenon. The obtained results provide a good viewpoint in using different models for studying propagation of the plane elastic waves in various particulate composites.

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.