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

Authors:	Jarroudi Mustapha El; Brillard Alain

Institution:	¹ Département de Mathématiques, Faculté des Sciences et Techniques, BP 416, Tanger, Morocco. Email: eljar{at}fstt.ac.ma ² Université de Haute-Alsace, 2 rue des Frères Lumière, F-68093 Mulhouse Cedex, France. Email: A.Brillard{at}uha.fr

Abstract:	We describe the asymptotic behaviour of a cylindrical elasticbody, reinforced along identical ${epsilon}$ -periodically distributed fibresof size r, with 0 < r < ${epsilon}$ , filled in with some differentelastic material, when this small parameter ${epsilon}$ goes to 0. Thecase of small deformations and small strains is considered.We exhibit a critical size of the fibres and a critical linkbetween the radius of the fibres and the size of the Lamécoefficients of the reinforcing elastic material. Epi-convergencearguments are used in order to prove this asymptotic behaviour.The proof is essentially based on the construction of appropriatetest functions.

Keywords:	reinforcement fibres linear elasticity epi-convergence
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