We obtain a nonlocal functional as the variational limit of an integral functional associated with the strain energy of a pseudo-plastic material reinforced by a epsilon-periodic distribution of pseudo plastic fibers. We begin by studying separately the variational limit behavior, when epsilon goes to zero, of the structure made of the soft material without fibers, and of the structure constituted by the distribution of the small fibers. We show that the complete structure is, in the sense of the Gamma-convergence, equivalent to a new homogeneous structure whose functional energy is the epigraphical sum of the limit integral functionals energies modeling each two previous structures.