Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

Shane Cooper

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.
Original languageEnglish
Pages (from-to)1401-1430
Number of pages29
JournalApplicable Analysis
Volume93
Issue number7
DOIs
Publication statusPublished - 10 Oct 2013

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