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arXiv · 1011.4367

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

Mustapha El Jarroudi·Alain Brillard
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Abstract

We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $ε$-periodically distributed fibers of size $r_ε$, with $0 < r_ε < ε$, 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.

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Mustapha El Jarroudi, Alain Brillard. 2010-11-19. Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers. https://doi.org/10.1093/imamat%2F66.6.567

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