Effect of an inhomogeneous interphase zone on the bulk modulus of a particulate composite containing spherical inclusions

The effects of an inhomogeneous interphase zone on the effective bulk modulus of particulate composites containing large concentrations of inclusions are analyzed. The composite is modeled as a suspension of elastic homogeneous hollow spherical particles in a continuous elastic matrix. An interphase zone surrounding inclusions where the matrix material has elastic moduli with radial variation that asymptotically assume a constant value far away from particles is then modeled. The related elastic problem of a single inclusion in a finite matrix subjected to a spherically symmetric load is considered and a closed-form solution in terms of hypergeometric functions is determined. This analytical solution is then employed to derive an explicit expression for the effective bulk modulus. A detailed parametric analysis is finally performed to investigate the influence of the geometric characteristics and elastic properties of the graded interphase zone for composites containing voids or solid/hollow inclusions.