Solutions to the periodic eshelby inclusion problem in two dimensions

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We solve the homogeneous Eshelby inclusion problem on a finite unit cell with periodic boundary conditions. The main result is a representation formula of the strain field which is reminiscent of the familiar Green's representation formula. The formula is valid for any smooth inclusion and divergence-free eigenstress. More, it is shown that a Vigdergauz structure does not have the Eshelby uniformity property for symmetric non-dilatational eigenstress unless it degenerates to a laminate.

Original languageEnglish (US)
Pages (from-to)557-590
Number of pages34
JournalMathematics and Mechanics of Solids
Volume15
Issue number5
DOIs
StatePublished - Jul 1 2010
Externally publishedYes

Fingerprint

Representation Formula
Two Dimensions
Inclusion
Green's Formula
Divergence-free
Laminates
Periodic Boundary Conditions
Uniformity
Boundary conditions
Valid
Unit
Cell

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mathematics(all)
  • Mechanics of Materials

Cite this

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Solutions to the periodic eshelby inclusion problem in two dimensions. / Liu, Liping.

In: Mathematics and Mechanics of Solids, Vol. 15, No. 5, 01.07.2010, p. 557-590.

Research output: Contribution to journalArticle

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