The present paper proposes an approximation of the influence of a small inhomogeneity, having different stiffness, in an elastic medium restricting its cinematics to a finite dimensional space. The problem, for the unknown displacement, is written in accordance of transmission conditions between elastic medium and inhomogeneity. The multi-scale asymptotic expansions techniques, by using some corrective terms, are introduced to analyze the inhomogeneity influence in both initial and approximated problems. Finally, some error estimates for asymptotic expansions are presented and different strategies are compared.

中文翻译：

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嵌入弹性介质中的小物体的厚点近似：渐近分析的证明

本论文提出了一种具有不同刚度的小不均匀性在弹性介质中的影响的近似值，该介质将其运动学限制在有限维空间中。该问题对于未知位移，是根据弹性介质与非均匀性之间的传递条件编写的。引入多尺度渐近展开技术，通过使用一些修正项，分析初始和近似问题中的不均匀性影响。最后，介绍了渐近扩展的一些误差估计，并比较了不同的策略。