Linear Heterogeneous Media: Multiscale Homogenization Approaches

Abstract

In this contribution, multi-scale asymptotic homogenization methods (AHM) are developed to find the effective properties of heterogeneous linear elastic structures. In particular, linear elastic micropolar and hierarchical periodic fiber-reinforced composites with square cells and perfect interface conditions are characterized. For both composites, the corresponding local problems on the periodic cell and the effective properties are determined, and closed form formulas are provided. In addition, we focused on antiplane local problems, which are stated and solved. The antiplane effective properties are also reported. Finally, the numerical results are presented and discussed. The influence of the fiber-matrix contrast and the fiber volume fraction on the antiplane effective behavior is evidenced.