沿同向纤维周期增强圆柱形弹性结构的渐近行为
Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers
摘要：
我们描述的渐近行为的圆柱形弹性体，加强沿相同的$ε$ -周期性分布的纤维尺寸$r_ε$，与$0 < r_ε < ε$，填充一些不同的弹性材料，当这个小参数$ε$去0。考虑了小变形和小应变的情况。我们展示了纤维的临界尺寸和纤维半径与增强弹性材料的Lamé系数的大小之间的关键联系。Epi-convergence参数，以证明这一渐近行为。证明基本上是基于适当的测试功能的建设。
英文摘要：
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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