Explicit elasticity–conductivity connections for composites with anisotropic inhomogeneities

Explicit elasticity–conductivity connections for anisotropic heterogeneous materials were recently derived and verified experimentally by the present authors. The constituents were assumed isotropic, so that the overall anisotropy was due solely due to nonrandom orientations of inhomogeneities. Motivated by the materials science applications that deal with strongly anisotropic inclusions, we derive alternative elasticity–conductivity connections that cover these cases. They hold for a broad class of orientation distributions—up to three families of parallel inhomogeneities forming arbitrary angles with each other, with moderate orientation scatter allowed in each of the families. In the case of the isotropic inhomogeneities, this form has substantially better accuracy than the approximate connections derived earlier. The results are compared with experimental data on fiber-reinforced plastics. The agreement is quite good for the entire set of the effective anisotropic constants, and it is achieved without any fitting parameters.