Homogenization of a nonlinear elastic structure periodically reinforced along identical fibres of high rigidity

We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical εε-periodically distributed fibres of size εε, filled in with some different elastic material, when this small parameter εε goes to 0. We suppose that both materials are nonlinear elastic ones, which means that their bulk energy is of Saint Venant–Kirchhoff type. Epi-convergence arguments are used in order to prove this asymptotic behaviour. The proof is essentially based on the construction of appropriate test-functions.