Simulation of the multi-scale convergence in computational homogenization approaches

Although the asymptotic homogenization is known to explicitly predict the thermo-mechanical behaviors of an overall structure as well as the microstructures, the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry. In order for the homogenization method for periodic media to apply for general heterogeneous ones, the problems arising from mathematical modeling are examined in the framework of representative volume element (RVE) analyses. Here, the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of RVE is sufficiently large. Then the numerical studies in this paper realize the multi-scale nature of the convergence of overall material properties as the unit cell size is increased. In addition to such dependency of the macroscopic field variables on the selected size of unit cells, the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method. Similar discussions are made for the elastoplastic mechanical responses in both macro- and microscopic levels. In these multi-scale numerical analyses, the specific effects of the microstructural morphology are reflected by using the digital image-based (DIB) finite element (FE) modeling technique which enables the construction of accurate microstructural models.