Homogenization of an elastic material reinforced with thin rigid von Karman ribbons

We study the homogenization of an elastic material reinforced with periodic parallel elastic ribbons of higher rigidity. We assume that the ribbons are isotropic von Karman plates of highly contrasting rigidity with respect to that of the matrix. We assume perfect adhesion along the common interface between the matrix and the ribbons. We derive effective energy functionals involving additional degrees of freedom implying nonlocal effects associated with thin boundary layer phenomena and additional integral terms, including macroscopic fields of extension, flexion and torsion.