A new approach to handle complex geometries in multi-scale analysis

International audienceIt is a common fact that as we go down to lower scales, the geometrical complexity rises eitherbecause of randomness or because of the heterogeneity of the micro-constituents, or both.This difficulty is on top of another more studied difficulty : how to bring the information of themicroscopic fields to the macro analysis (“homogenization”) and, vice-versa, how to localizethe macro-field to a small region of interest (“localization”).The presentation will focus on the two preceeding issues using the so-called eXtended Finite Elementapproach (X-FEM). This approach was initially developped to describe cracks on mesheswhich are not conforming to the cracks