Application of multi-scale modelling to some elastic, piezoelectric and electromagnetic composites

One way to obtain new materials is to mix classical ones with periodic heterogeneous microstructures. Using the homogenization method, we rigorously justify the limit models obtained ( when the size of the microstructures goes to zero) for composites with very promising properties. We present here three different examples: a new bio-compatible piezoelectric/living cells material designed to improve bone regeneration, a bianisotropic electromagnetic material in a first attempt of photonic crystals modelling and a strongly heterogeneous elastic material exhibiting acoustic band-gaps. We also provide numerical simulations in order to illustrate the influence of the change of intrinsic parameters such as shape and physical characteristics of the micro structures.