Abstract
The homogenization method is examined in conjunction with the method of representative volume elements (RVE). When the digital image-based modeling technique enables us to model the complex geometry of microstructures, the boundaries of unit cells fail to have the geometric periodicity Nonetheles, the effective moduli are reasonably estimated by the homogenition with periodic boundary conditions. This fact is justified theoretically and simulated along with the notion of homogenization convergence. In adition to the convegence of effective moduli with respect to the size of RVEs, the microscopic mechanical behaviors are examined in comparison with macroscopic ones. Thus, the multiscale nature of the analysis modeling by the asymptotic homogenization is characterized by carrying out a series of linear and nonliinear numerical analyses.
