MULTI-SCALE MODELING APPLIED TO NON LINEAR CONSTITUTIVE EQUATIONS

Several multi-scale approaches have been developed at Onera in order to describe as accurately as possible the non linear behavior of materials with complex microstructures. These developments are conducted in conjunction with experimental observations that are more and more sophisticated leading to very precise information at the local scale. The interaction between the modeling and the experimental techniques facilitate the identification of material parameters. Two main ways are proposed to perform the multi -scale analysis. The first one called "integrated approach" consists to compute the macroscopic response and the local one at the same time using an imbricated finite element scheme. The second way called "sequential approach" consists to establish macroscopic constitutive equations from a multi -scale technique generally based on a mean field approach. This way is close to a phenomenological one but is richest allowing the possibility to determine the local fields in the microstructure using post-processing tools.