El Jarroudi, Mustapha; Brillard, Alain Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibres. (English) Zbl 1016.74053 IMA J. Appl. Math. 66, No. 6, 567-590 (2001). Summary: We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical \(\varepsilon\)-periodically distributed fibres of size \(r_\varepsilon\), with \(0<r_\varepsilon <\varepsilon\), filled in with some different elastic material, when this small parameter \(\varepsilon\) 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 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. Cited in 15 Documents MSC: 74Q05 Homogenization in equilibrium problems of solid mechanics 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 74E30 Composite and mixture properties Keywords:cylindrical elastic structure; reinforcement; linear elasticity; epi-convergence; periodically distributed fibres; asymptotic behaviour PDFBibTeX XMLCite \textit{M. El Jarroudi} and \textit{A. Brillard}, IMA J. Appl. Math. 66, No. 6, 567--590 (2001; Zbl 1016.74053) Full Text: DOI arXiv