EXACT RELATIONS BETWEEN MACROSCOPIC MODULI OF COMPOSITE MEDIA IN n DIMENSIONS

摘要

Generic n-dimensional (nD) exact relations are found between macroscopic or bulk effective moduli of composite systems with related microstructures. These relations can be established between effective values of material coefficients of the same type (e.g. conductivity and conductivity) as well as between different types of material coefficients (e.g. conductivity and permittivity). As example of possible application of these relations, a set of Keller-like quasi-3D relations are derived for the case of columnar-shaped parallel inclusions. The microstructure in the two samples can, in general, be different. Those relations are tested by comparing with a number of numerical calculations of macroscopic dc and ac response in such systems.