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

    17 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

    Bibliographical note

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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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