Effective moduli of particle-filled composite with inhomogeneous interphase: Part I – bounds

This part of the two-part paper reports calculations for the effective moduli of a particle-filled composite with the properties of the interphase continuously varying in the radial direction. First, the difficulties in obtaining the explicit expressions of the effective moduli are explained. Then by using the generalized self-consistent method (GSCM) and by introducing an inhomogeneous comparison material with a microstructure different from that of the real material, explicit expressions of the upper and lower bounds of the effective moduli for the composite are obtained. These bounds are found to be very close for the considered case. The comparison of the explicit bounds with the numerical results shows that the present solutions are satisfactory.