Solutions of inhomogeneity problems with graded shells and application to core-shell nanoparticles and composites

H. L. Duan, Y. Jiao, X. Yi, Z. P. Huang, J. Wang

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


This paper first presents the Eshelby tensors and stress concentration tensors for a spherical inhomogeneity with a graded shell embedded in an alien infinite matrix. The solution is then specialized to inhomogeneous inclusions in finite spherical domains with fixed displacement or traction-free boundary conditions. The Eshelby tensors in the infinite and finite domains and the stress concentration tensors are especially useful for solving many problems in mechanics and materials science. This is demonstrated on two examples. In the first example, the strain distributions in core-shell nanoparticles with eigenstrains induced by lattice mismatches are calculated using the Eshelby tensors in the finite domains. In the second example, the Eshelby and stress concentration tensors in the three-phase configuration are used to formulate the generalized self-consistent prediction of the effective moduli of composites containing spherical particles within the framework of the equivalent inclusion method. The advantage of this micromechanical scheme is that, whilst its predictions are almost identical to the classical generalized self-consistent method and the third-order approximation, the expressions for the effective moduli have simple closed forms.

Original languageEnglish (US)
Pages (from-to)1401-1425
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number7
StatePublished - Jul 2006
Externally publishedYes


  • Core-shell nanoparticle
  • Effective modulus
  • Eshelby tensor
  • Finite domain
  • Stress concentration tensor

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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