Multiple scattering of elastic waves in metal-matrix composite materials with high volume concentration of particles

A new approach is proposed to investigate the propagation of compressional (P) and shear (SV) waves in metal-matrix composite materials with high volume concentration of particles. The theory of quasicrystalline approximation and Waterman's T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The analytical expression of the Percus–Yevick correlation function is also given. Closed form solutions for the effective propagation constants and the dynamic effective elastic modulus of materials are obtained in the low frequency limit. At higher frequencies, only numerical results of them are presented. Numerical examples show that the phase velocities of P and SV waves in the composite materials with low volume concentration in the low frequency are in good agreement with the results in previous literatures. The effects of the incident wave number, the volume fraction of particles and the material properties of the particles and matrix on the dynamic effective elastic modulus are also examined.