Résumé
By using ergodic theory and a variational process, we study the macroscopic behavior of a thin body with micro hight stiffness fibers randomly distributed according to a stationary point process. The thickness of the body, the stiffness and the size of the cross sections of the fibers depend on a small parameter ε. The variational limit functional energy obtained when ε tends to 0 is deterministic and depends on two variables: one is the deformation of a two dimensional body and describes the behavior of the medium in the matrix, the other captures the limit behavior of deformations in the fibers when the thickness, the stiffness and the size section become increasingly thin.