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

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

2010-11-19

arxiv.org/abs/1011.4367v1

IMA Journal of Applied Mathematics 66, 6 (2001) 567-590

Mathematics

Analysis of PDEs

Scientific paper

10.1093/imamat/66.6.567

We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $\epsilon$-periodically distributed fibers of size $r_{\epsilon}$, with $0 < r_{\epsilon} < \epsilon$, filled in with some different elastic material, when this small parameter $\epsilon$ 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 Lam\'e 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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