Comparison of unit cell and windowing methods for obtaining estimates on macroscopic elasticity tensors of inhomogeneous materials

Two methods for estimating the macroscopic elastic tensors of discrete inhomogeneous microgeometries, periodic homogenization and "windowing", are compared. Periodic homogenization can be used for any material symmetry but requires periodic volume elements, also known as unit cells. Windowing does not pose periodicity requirements and, when using specific mixed uniform boundary conditions, gives identical results to periodicity boundary conditions for orthotropy or higher material symmetries. The present contribution studies the applicability of the latter approach to volume elements that show some sub-orthotropic contributions to their macroscopic symmetry. For this purpose both periodic homogenization and windowing are applied to unit cells that are aimed at describing macroscopically isotropic particle reinforced composites but are known to have limited lowsymmetry contributions to their macroscopic elastic behavior. Good agreement between the two Finite Element based modeling approaches is found, indicating the applicability of the windowing approach to volume elements that approach, but do not fulfill geometrical orthotropy.