Effective longitudinal wave in an elastic matrix containing coated or uncoated spheres: Influence of the second order approximation including multiple scattering

Some properties of the effective longitudinal (L) wave propagating in an elastic matrix containing a random distribution of coated or uncoated spheres are investigated. The multiple scattering between spheres is taken into account by considering a second order corrective term in concentration. According to Luppé, Conoir and Norris (J. Acoust. Soc. Am. 131 (2012) 1113–1120) this term contains the coupling between L and T (transverse) waves occurring at each scattering event, which is usually not considered in many works. Numerical computations of phase velocity and attenuation of the effective longitudinal wave are provided for an epoxy matrix. Several specific topics are reviewed such as the role of: the sphere material (glass, steel and lead), the thickness of the rubber coating, the L→L, L→T and T→L mode conversions in the multiple scattering corrective term and in the effective longitudinal wave. Formulas for the effective wavenumber, bulk modulus and mass density of the composite are provided in the Rayleigh limit for the case of uncoated spheres.