Effective stiffness tensor of composite media: II. Applications to isotropic dispersions

Accurate approximate relations for the effective elastic moduli of two- and three-dimensional isotropic dispersions are obtained by truncating, after third-order terms, an exact series expansion for the effective stiffness tensor of d-dimensional two-phase composites (obtained in the first paper) that perturbs about certain optimal dispersions. Our third-order approximations of the effective bulk modulus K_e and shear modulus G_e are compared to benchmark data, rigorous bounds and popular self-consistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third-order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to popular self-consistent approximations.