Present experimental facilities give local insight on the physical mechanisms which govern the detailed mechanical response of advanced or complex materials such as functionalized or reinforced polymers, flexible semiconductors, microarchitectured materials or geomaterials. This will be illustrated in our talk by various examples studied in our laboratory. Such results can reduce the level of arbitration encountered in the construction of relevant macroscopic models and can explain the evolutive anisotropy which occurs in damage or in phase transitions. But for this purpose, one must develop adequate strategies relating microscopic and macroscopic models.
The second part of the talk will illustrate this multiscale dialog in polymer modelling. The difficulty there is to pass from one chain to a network of cross-linked chains, and to relate the evolution of this network to the macroscopic deformation. The use of a microscopic network problem imposing the macroscopic deformation through a far field microscopic boundary condition is a mathematically rigorous and attractive approach, but it is practically out of reach because of its complexity and because of modeling issues (carbon fillers, strain induced crystallization, damage, …). A simpler strategy is to reduce the microstructure to a distribution of one dimensional stress strain relations over the orientation space. Such microsphere approaches have been used successfully in the past to describe complex phenomena such as Mullins effect or strain induced crystallization. This leads to evolutive anisotropic models which respect the experimental data available at microscopic level, but up to now the different local orientations were related to the 3D deformation through a simplified affine network deformation assumption. The talk will review these approaches and explain how to go beyond the affine assumption by introducing a proper free energy to be minimized locally, the macroscopic deformation being introduced as a maximal path constraint.