Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers

Mustapha El Jarroudi (1) , Alain Brillard (2)

1 FST Tanger, Département de Mathématiques - Facullté des Sciences et Techniques Tanger, Département de Mathématiques
2 GRE - Laboratoire de Gestion des Risques et Environnement

We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical ε-periodically distributed fibers 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 fibers and a critical link between the radius of the fibers 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.

Mots clés: Reinforcement; fibers; linear elasticity; epi-convergence

Domaines: Equations aux dérivées partielles [math.AP]

Mustapha El Jarroudi, Alain Brillard. Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers. IMA Journal of Applied Mathematics, 2001, 66 (6), pp.567-590. ⟨10.1093/imamat/66.6.567⟩. ⟨hal-00536346⟩