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A generalized differential effective medium theory. (English) Zbl 0579.73114
Summary: A generalization of the differential effective medium approximation (DEM) is discussed. The new scheme is applied to the estimation of the effective permittivity of a two phase dielectric composite. Ordinary DEM corresponds to a realizable microgeometry in which the composite is built up incrementally through a process of homogenization, with one phase always in dilute suspension and the other phase associated with the percolating backbone. The generalization of DEM assumes a third phase which acts as a backbone. The other two phases are progressively added to the backbone such that each addition is in an effectively homogeneous medium. A canonical ordinary differential equation is derived which describes the change in material properties as a function of the volume concentration \(\phi\) of the added phases in the composite. As \(\phi\) \(\to 1\), the effective medium approximation (EMA) is obtained. For \(\phi <1\), the result depends upon the backbone and the mixture path that is followed. The approach to EMA for \(\phi\) \(\cong 1\) is analysed and a generalization of Archie’s law for conductor-insulator composites is described. The conductivity mimics EMA above the percolation threshold and DEM as the conducting phase vanishes.

74F15 Electromagnetic effects in solid mechanics
74E05 Inhomogeneity in solid mechanics
74A40 Random materials and composite materials
Full Text: DOI
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