MULTIPLE-SCATTERING THEORY FOR DISCRETE, ELASTIC, RANDOM-MEDIA

A theory is presented for determining the ensemble-averaged Green tensor of a statistically homogeneous distribution of identical, randomly oriented elastic scatterers embedded in an infinite, homogeneous, and isotropic matrix. The theory is based on the self-consistent formulation of Lax's [Rev. Mod. Phys. 23, 287 (1951); Phys. Rev. 85, 621 (1952)] multiple scattering theory due to Gyorffy [Phys. Rev. B 1, 3290 (1970)] and Korringa and Mills [Phys. Rev. B 5,1654 (1972)]. The average Green tensor is found to be characterized by three parameters which may depend on the momentum operator but which are otherwise analogous to the Lamé constants and density of an ideal, homogeneous, and isotropic medium. These effective" parameters are shown to be related in the usual way to the wave numbers of coherent compressional and shear plane-wave modes of the random composite. The ensemble averaged Green tensor and the dispersion relations satisfied by the wave numbers of the coherent modes are found to depend on the single and joint probability density functions for the scattering centers and on the transition operator of a discrete scatterer embedded in the effective (average) medium. The dispersion relations are evaluated explicitly for the limiting case of a completely random ensemble of homogeneous and isotropic scatterers whose elastic parameters and density differ very little from those of the matrix medium. © 1980 American Institute of Physics."