Multiple scattering of elastic waves in a fiber-reinforced composite
This paper considers elastic wave propagation in fibre-reinforced composites that consist of a homogeneous, isotropic matrix medium containing long parallel, randomly distributed circular fibres having identical properties. Two particular problems are investigated. In one an \(SH\) wave propagates perpendicular to the fibres with particle motion parallel to the fibres while in the other a \(P\) or \(SV\) wave propagates perpendicular to the fibres with particle motion also perpendicular to the fibres. To allow for multiple scattering phenomena at high fibre concentrations, the authors employ a method that combines the so-called `generalized self-consistent model' together with a well used statistical averaging procedure [e.g. see \textit{P. C. Waterman} and \textit{R. Truell}, J. Math. Phys. 2, 512-537 (1961; Zbl 0108.21403)] to calculate the effective dynamic constants of the composite. Numerical results are presented for both graphite-epoxy and silicon carbide-titanium composites with the effective phase velocity and attenuation of the coherent waves being calculated for a wide range of frequencies and concentrations. Furthermore, the degree of interaction between the fibres is determined and the values for the average strain in a given inclusion obtained by both direct analysis and approximate homogenisation are compared. Unlike previous studies (e.g. loc. cit.), the method proposed by the authors recovers all the well-known effective moduli of fibre reinforced composites in the static limit and appears to give reasonable results at both higher concentrations and frequencies.
scientific article; zbMATH DE number 754639
scientific article