The bounds on the effective conductivities of heterogeneous media containing discretely suspended particles with a graded interphase or graded particles are presented through introducing comparison materials. The microstructures of the comparison materials are different from those of the considered heterogeneous media. The comparison materials provide a means of obtaining optimized narrow bounds. The effective conductivities of these composites are also predicted using the composite sphere assemblage (CSA) model. It is shown that the CSA predictions are within the appropriate bounds for the considered media.

• Received 10 September 2005

DOI:https://doi.org/10.1103/PhysRevB.73.104208