On Scale Transition and Homogenization in Multiscale Computational Analysis of Heterogeneous Solids

A detailed study of the scale transition in the asymptotic multiscale analysis of heterogeneous solids is presented. Through a one-dimensional periodic model problem with analytical solution, the micro scale analysis of unit cell and coarse-graining analysis for homogenized material constants, especially the scale transition, are discussed in details. The relationship between the asymptotic expansion multiscale method and variational multiscale method is also illustrated. Meanwhile two dimensional numerical experiments are performed to justify the unit cell performance for periodic problems.