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

Hyeonbae Kang, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish
Article number22
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number1
DOIs
Publication statusPublished - 2020 Feb 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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