A simple model for elastic wave propagation in hard sphere-filled random composites

Abstract

A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4–5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.