Semi-analytic solution for multiple interacting three-dimensional inhomogeneous inclusions of arbitrary shape in an infinite space

Kun Zhou*, Leon M. Keer, Q. Jane Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

76 Scopus citations

Abstract

This paper develops a semi-analytic solution for multiple arbitrarily shaped three-dimensional inhomogeneous inclusions embedded in an infinite isotropic matrix under external load. All interactions between the inhomogeneous inclusions are taken into account in this solution. The inhomogeneous inclusions are discretized into small cuboidal elements, each of which is treated as a cuboidal inclusion with initial eigenstrain plus unknown equivalent eigenstrain according to the Equivalent Inclusion Method. All the unknown equivalent eigenstrains are determined by solving a set of simultaneous constitutive equations established for each equivalent cuboidal inclusion. The final solution is obtained by summing up the closed-form solutions for each individual equivalent cuboidal inclusion in an infinite space. The solution evaluation is performed by application of the fast Fourier transform algorithm, which greatly increases the computational efficiency. Finally, the solution is validated by taking Eshelby's analytic solution of an ellipsoidal inhomogeneous inclusion as a benchmark and by the finite element analysis. A few sample results are also given to demonstrate the generality of the solution. The solution may have potentially significant applications in solving a wide range of inhomogeneity-related problems.

Original languageEnglish (US)
Pages (from-to)617-638
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Volume87
Issue number7
DOIs
StatePublished - Aug 19 2011

Keywords

  • Arbitrary shape
  • Equivalent inclusion method
  • Fast Fourier transform
  • Inhomogeneity
  • Inhomogeneous inclusion
  • Three-dimensional

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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