Homogenization model for a dense elastic medium of cylindrical scatterers and based on a realistic pair correlation function

Abstract

Multiple scattering effects due to a random distribution of identical cylindrical inclusions in an elastic medium are investigated. The approach is based on the analysis proposed by Fikioris and Waterman. The solution of the developed modal equations yields the effective wavenumbers of elastic coherent waves. Attention is made in this paper to a more realistic description of scatterers’ distribution in the host medium: this distribution is taken into account in modeling by introducing the notion of pair correlation function. The existing Conoir and Norris approach has been established by using the Hole Correction as pair correlation function, which simplifies the description of scatterers’ distribution and may lead to unphysical results for dense media. New formulas for the effective wavenumbers are proposed here by generalization of the latter theory and enable the use of any pair correlation function for possible application to dense media. The new generalized analytical model coupled to a realistic pair correlation function is compared to the previous approach in different materials configurations and validated for concrete structures by comparison to numerical simulations.