Analytical homogenization of linear elasticity based on the interface orientation distribution – A complement to the self-consistent approach

We combine a laminate-based approach and an interface orientation average. For linear elasticity, we obtain analytical expressions for the effective stiffness of mixtures of two isotropic phases with isotropic, transversely isotropic, hexahedral and octahedral interface orientation distributions (IOD). The estimates are in accordance with well-established analytical results such as the Hashin–Shtrikman bounds and Hill’s findings for phases with equal shear moduli.For isotropic and transversely isotropic IODs, this approach is compared to the Hashin–Shtrikman bounds and the inclusion-based self-consistent approach. At extremal volume fractions, both approaches coincide up to first order with complementary and mixed Hashin–Shtrikman-bounds. Thus, our approach provides an alternative to the self-consistent approach.Moreover, the effective stiffness inherits any symmetry of the IOD. Therefore, it captures basic features of the morphology-induced anisotropy.For the hexahedral and octahedral IOD, the approach is compared to RVE simulations. To assess the impact of morphological features beyond the IOD, we consider RVEs with different microstructures but equal IOD. Comparing similar microstructures, the error attains a local minimum close to the point of equal arrangement of phases. Further, we find a reasonable agreement if the shear moduli are of the same order of magnitude or if both phases percolate the material.