In the present work, approximate connections between two groups of anisotropic effective properties – conductivity and elasticity - are derived and specified for several heterogeneous anisotropic microstructures and verified by comparison with experimental data. The elasticity tensor is expressed in terms of the conductivity tensor in the closed form. The cross-property connections are derived in the framework of non-interaction approximation. In the cases when the interactions between inhomogeneities cannot be neglected, we hypothesize that the interactions affect both groups of properties – elastic and conductive – in a similar way, so that the cross-property correlations continue to hold, although this approximation may yield substantial errors for each of the properties separately (this idea was first suggested by Bristow, 1960 for a material with randomly oriented microcracks). This assumption is confirmed by comparison with experimental data on various materials: plasma sprayed ceramic coatings, short glass fiber reinforced thermoplastics and aluminum foams. The similar type of cross-property connection is obtained also for granular materials.
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