Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

Qinghua Zhou, Xiaoqing Jin*, Zhanjiang Wang, Jiaxu Wang, Leon M. Keer, Qian Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A new numerical method for solving two-dimensional arbitrarily shaped inhomogeneity problems is demonstrated in the present work. Solution is achieved through a discretization consisting of rectangular elements using newly formulated closed-form solutions. An iterative scheme for implementing the numerical equivalent inclusion method, i.e., determining the equivalent eigenstrains, is proposed. Comprehensive benchmarks on numerical convergence with respect to mesh size and iterative number are conducted to demonstrate the performance of the new numerical method. Comparative studies among results are obtained by the proposed iterative scheme, the Gaussian elimination method, and the Hutchinson approximation and show superiority of the iterative scheme. Simulations for material combinations utilizing the Dundurs α–β plane reveal its capability. A double-inhomogeneity model illustrates the ability of the new numerical method to predict the stress concentration factor for closely distributed multiple inhomogeneities.

Original languageEnglish (US)
Pages (from-to)39-61
Number of pages23
JournalJournal of Elasticity
Issue number1
StatePublished - Jan 2015


  • Inclusion solution
  • Inhomogeneity
  • Numerical equivalent inclusion method
  • Stress concentration factor

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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