Circular inhomogeneity with Steigmann–Ogden interface: Local fields, neutrality, and Maxwell's type approximation formula

Anna Y. Zemlyanova, Sofia G. Mogilevskaya

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67 Scopus citations


The boundary conditions for the Steigmann–Ogden (1997, 1999) model are re-derived for a two dimensional surface using general expression for surface energy that include surface tension. The model treats the interface as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffness. The two-dimensional plane strain problem of an infinite isotropic elastic domain subjected to the uniform far-field load and containing an isotropic elastic circular inhomogeneity whose interface is described by the Steigmann–Ogden model is solved analytically. Closed-form expressions for all elastic fields in the domain are obtained. Dimensionless parameters that govern the problem are identified. The Maxwell type approximation formula is obtained for the effective plane strain properties of the transversely isotropic materials containing multiple inhomogeneities with the Steigmann–Ogden interfaces. The “neutrality” conditions are analyzed. It is demonstrated that while the Steigmann–Ogden model theoretically reduces to the Gurtin–Murdoch (1975, 1978) model when the bending interphase effects are neglected, the two models (for the case of zero surface tension) describe two very different interphase regimes of seven regimes proposed by Benveniste and Miloh (2001).

Original languageEnglish (US)
Pages (from-to)85-98
Number of pages14
JournalInternational Journal of Solids and Structures
StatePublished - Mar 15 2018

Bibliographical note

Funding Information:
The first author (A.Z.) gratefully acknowledges the support from Simons Collaboration grant, award number 319217. The second author (S.M.) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota.

Publisher Copyright:
© 2017 Elsevier Ltd


  • Circular inhomogeneity
  • Effective properties
  • Steigmann–Ogden model
  • Surface effects


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