Interphase zone effect on the spherically symmetric elastic response of a composite material reinforced by spherical inclusions

This work deals with the problem of modeling the effect due to an interphase zone between inclusion and matrix in particulate composites to better estimate the bulk modulus of materials with inclusions. To this end, in this paper the problem of a body containing a hollow or solid spherical inclusion subjected to a spherically symmetric loading is investigated in the framework of the elasticity theory. The interphase zone around the inclusion is modeled by considering the elastic properties varying with the radius moving away from the interface with inclusion and, asymptotically approaching the value of the homogeneous matrix. The explicit solutions are obtained in closed form by using hypergeometric functions and numerical investigations are performed to highlight the localized effects of the graded interphase in the stress transfer between inclusion and matrix. Finally, the exact solutions are used to estimate the effective bulk modulus of a material containing a dispersion of hollow or solid spherical inclusions with graded interphase zone.