Solutions to the periodic eshelby inclusion problem in two dimensions

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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
Issue number5
StatePublished - Jul 1 2010
Externally publishedYes


All Science Journal Classification (ASJC) codes

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


  • Complex variable method
  • Eshelby inclusion problem
  • Periodic inclusions

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