The principle of equivalent eigenstrain for inhomogeneous inclusion problems

Lifeng Ma, Alexander M. Korsunsky

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


In this paper, based on the principle of virtual work, we formulate the equivalent eigenstrain approach for inhomogeneous inclusions. It allows calculating the elastic deformation of an arbitrarily connected and shaped inhomogeneous inclusion, by replacing it with an equivalent homogeneous inclusion problem, whose eigenstrain distribution is determined by an integral equation. The equivalent homogeneous inclusion problem has an explicit solution in terms of a definite integral. The approach allows solving the problems about inclusions of arbitrary shape, multiple inclusion problems, and lends itself to residual stress analysis in non-uniform, heterogeneous media. The fundamental formulation introduced here will find application in the mechanics of composites, inclusions, phase transformation analysis, plasticity, fracture mechanics, etc.

Original languageEnglish
Pages (from-to)4477-4484
Number of pages8
JournalInternational Journal of Solids and Structures
Issue number25-26
Publication statusPublished - 1 Dec 2014
Externally publishedYes


  • Inhomogeneous inclusion
  • Integral equation
  • Residual strain
  • The equivalent eigenstrain method


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