Effect of the interphase zone on the bulk modulus of a particulate composite

An exact solution is found for the problem of hydrostatic compression of an infinite body containing a spherical inclusion, with the elastic moduli varying with radius outside of the inclusion. This may represent an interphase zone in a composite, or the transition zone around an aggregate particle in concrete, for example. Both the shear and the bulk moduli are assumed to be equal to a constant term plus a power-law term that decays away from the inclusion. The method of Frobenius series is used to generate an exact solution far the displacements and stresses. The solution is then used to estimate the effective bulk modulus of a material containing a random dispersion of these inclusions. The results demonstrate the manner in which a localized interphase zone around an inclusion may markedly affect both the stress concentrations at the interface, and the overall bulk modulus of the material.