Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibres
Mustapha El Jarroudi · IMA Journal of Applied Mathematics · 2001
We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical ε‐periodically distributed fibres of size rε, with 0 < rε < ε, filled in with some different elastic material, when this small parameter ε goes to 0. The case of small deformations and small strains is considered. We exhibit a critical size of the fibres and a critical link between the radius of the fibres and the size of the Lamé coefficients of the reinforcing elastic material. Epi‐convergence arguments are used in order to prove this asymptotic behaviour. The proof is essentially based on the construction of appropriate test functions.