Calculation of effective properties of composite materials with periodic microstructures using the Asymptotic Homogenization Method

Mean-field estimates of effective material properties of periodic structures using the Mori-Tanaka (MT) method fail to capture the interparticle interactions at higher inclusion volume fractions. The finite element based asymptotic homogenization method (AHM), serves as a robust numerical tool in this regard. Assuming there exists a substantial separation of length scales between the macroscopic and microscopic structures, the perturbations of the potential field caused due to the presence of inclusion under a macroscopic loading are used to predict the effective property. This method is utilised to study the effective electrical conductivity in fibrous systems and compared against existing MT estimates. For spherical inclusions, the study revealed that MT estimate and AHM agree well at volume fractions less than 0.4. However, near maximum packing fractions, AHM results fared significantly better than MT when compared with known asymptotic forms (Keller 1963). The current work aims at implementing the proposed AHM method to structures with aligned spheroidal inclusions of various aspect ratios and conductivity ratios, thus providing a more generalized approach to predict the effective electrical conductivity.