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首页> 外文期刊>European Journal of Mechanics. A, Solids >Local and global effects of small holes periodically distributed on a surface embedded in an axisymmetrical elastic medium
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Local and global effects of small holes periodically distributed on a surface embedded in an axisymmetrical elastic medium

机译：周期性地分布在嵌入轴对称弹性介质中的表面上的小孔的局部和整体效应

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摘要

We study an axisymmetric structure made of a linearly isotropic and homogeneous elastic material containing small holes whose centers are periodically distributed on a surface. The global structure then consists of two homogeneous media connected by a thin pierced layer which contains the holes. We use a multiple scaling method involving both periodic homogenization and matched asymptotic expansions. We aim at obtaining on the one hand the stresses close to the holes, and on the other hand the global behavior of the body. The stress field in the neighborhood of the hole is obtained through the solution of three elastic problems posed in an infinite strip containing a hole. It also allows to calculate the coefficients entering into the effective behaviour of the body. These coefficients depend on the shape of the holes. The second order problem involves jumps of the displacement and the stress fields which depend on the first order terms, and which exhibit singularities.
机译：我们研究了由线性各向同性和均质弹性材料制成的轴对称结构，该材料包含中心周期性分布在表面上的小孔。然后，整体结构由两个均质介质组成，该均质介质由包含孔的薄穿孔层连接。我们使用涉及周期性均质化和匹配渐近展开的多重缩放方法。我们的目标是一方面获得靠近孔的应力，另一方面获得身体的整体行为。孔附近的应力场是通过解决包含孔的无限条带中的三个弹性问题而获得的。它还允许计算进入人体有效行为的系数。这些系数取决于孔的形状。二阶问题涉及位移和应力场的跳跃，这些位移和应力场取决于一阶项，并且表现出奇异性。

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