Macroscopic behavior of a randomly fibered medium

By combining variational convergence with ergodic theory of subadditive processes, we study the macroscopic behavior of a randomly fibered medium. The cross sections of the fibers are randomly distributed according to a stationary point process, their size is of order ε while the stiffness of the material in the matrix is of order εp. The variational limit functional energy obtained when ε tends to 0 is deterministic and non local.