Micro-based enriched multiscale homogenization method for analysis of heterogeneous materials

Abstract

The aim of this contribution is to present a multiscale framework that incorporates required spatial distribution of strain field from RVE into the macro level by adoption of appropriate enrichment functions and corresponding additional kinematic variables from the RVE level. The basic idea of macroscopic kinematic variable in advanced multiscale homogenization methods is comprehensively examined, and while the macro-based approach has been available in the literature, the new proposed micro-based scheme is explored in this study. Furthermore, the proposed approach is employed to formulate the new “Enriched MultiScale Homogenization Method (EMSHM)”, based on the micro-based scheme. The key steps of adoption of appropriate additional kinematic variables, scale transition procedure and applying boundary conditions are also explained. Afterwards, EMSHM is applied to cases of cracked RVEs and severe strain gradient in the vicinity of macroscopic crack, with the inspiration of Heaviside (H-EMSHM) and crack tip (T-EMSHM) enrichments of the extended numerical methods. Accuracy of H-EMSHM with respect to the direct numerical modeling is explained with one and two dimensional examples. Numerical results of T-EMSHM have shown superior advantageous over the first order homogenization method from both the spatial distribution and magnitude of stress near the macro crack tip region.