Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity

L. Tian, R. K. N. D. Rajapakse

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145 Citations (Scopus)


Two-dimensional elastic field of a nanoscale circular hole/inhomogeneity in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. A closed-form analytical solution is obtained by using the complex potential function method of Muskhelishvili. Selected numerical results are presented to investigate the size dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. Stress state is found to depend on the radius of the inhomogeneity/hole, surface elastic constants, surface residual stress, and magnitude of far-field loading.
Original languageEnglish
Pages (from-to)568-574
Number of pages7
JournalJournal of Applied Mechanics
Issue number3
Publication statusPublished - 31 May 2007


  • nanostructured materials
  • elastic moduli
  • stress


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