On the effective properties of random microstructures and cross-property connections for them

Effective elastic and conductive properties of 2-D random (“disordered”) mixtures of several types are examined by computational means. It is found that an “equivalent” material of simple microgeometry – a continuous matrix with elliptical inhomogeneities – can be identified, that matches both the elastic and the conductive properties, in the entire range of property contrast between constituents. Moreover, the ellipse eccentricities are almost the same for different types of the random mixtures in the volume fraction range (0.3 – 0.7); in this range, there is no need in specifying the type of a mixture, as far as the effective properties are concerned. It is also found that the effective properties of the considered random mixtures are well described by the Mori-Tanaka-Benveniste model (in spite of the fact that this model was not intended for them).

We also examined the effect of inhomogeneity interactions in a matrix composite on the cross-property connections between the elastic and conductive properties. Whereas the interactions generally produce strong effect on each of the properties, their effect on the connections is negligible (the latter can be taken from the non-interaction approximation).

It is argued that most findings related to 2-D random mixtures should apply to 3-D ones as well.