关于密排弹性复合材料有效性能的Flaherty-Keller公式的证明
A proof of the Flaherty-Keller formula on the effective property of densely packed elastic composites
摘要：
用严格的数学方法证明了Flaherty和Keller关于含硬夹杂的密集周期弹性复合材料有效性质的渐近公式。证明是基于原始-对偶变分原理，其中上界是由Keller型检验函数和下界由应变核的奇异函数导出。奇异函数是Lamé系统的解，精确地捕捉了两个相邻硬夹杂之间狭窄区域内应力的奇异行为。
英文摘要：
We prove in a mathematically rigorous way the asymptotic formula of Flaherty and Keller on the effective property of densely packed periodic elastic composites with hard inclusions. The proof is based on the primal-dual variational principle, where the upper bound is derived by using the Keller-type test functions and the lower bound by singular functions made of nuclei of strain. Singular functions are solutions of the Lamé system and capture precisely singular behavior of the stress in the narrow region between two adjacent hard inclusions.
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