In this thesis we study some macroscopic models for drivers or elastic media highly heterogeneous and anisotropic obtained by homogenization. We consider the case of periodic homogenization. In particular the system of linearized elasticity modeling small deformations of a fiber material, we study the effect of material anisotropy on the macroscopic model and show that the combined effect of the boundary conditions and the anisotropy of the fiber system modeling movement at the macroscopic scale involves non-standard terms. We consider several scalings and two geometric situations: in the first radius of cylindrical fibers is of the same order of magnitude as the size of the middle period and in the second the radius is small compared to the period. The results obtained in both cases, independent of symmetry assumptions on the material used to find the results already known in the case of isotropic materials.
