A proof of the Flaherty–Keller formula on the effective property of densely packed elastic composites

Hyeonbae Kang; Sanghyeon Yu

doi:10.1007/s00526-019-1692-z

A proof of the Flaherty–Keller formula on the effective property of densely packed elastic composites

Hyeonbae Kang, Sanghyeon Yu

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

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.

Original language	English
Article number	22
Journal	Calculus of Variations and Partial Differential Equations
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s00526-019-1692-z
Publication status	Published - 2020 Feb 1

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-019-1692-z

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A proof of the Flaherty–Keller formula on the effective property of densely packed elastic composites

Abstract

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