On spherical inhomogeneity with Steigmann-Ogden interface

Anna Y. Zemlyanova, Sofia G. Mogilevskaya

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The problem of an infinite isotropic elastic space subjected to uniform far-field load and containing an isotropic elastic spherical inhomogeneity with Steigmann-Ogden interface is considered. The interface is treated as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffnesses. The constitutive and equilibrium equations of the Steigmann-Ogden theory for a spherical surface are written in explicit forms. Closed-form analytical solutions are derived for two cases of loading conditions-the hydrostatic loading and deviatoric loading with vanishing surface tension. The single inhomogeneity-based estimates of the effective properties of macroscopically isotropic materials containing spherical inhomogeneities with Steigmann-Ogden interfaces are presented. It is demonstrated that, in the case of vanishing surface tension, the Steigmann-Ogden model describes a special case of thin and stiff uniform interphase layer.

Original languageEnglish (US)
Article number121009
JournalJournal of Applied Mechanics, Transactions ASME
Issue number12
StatePublished - Dec 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. We also would like to express our gratitude to Mr. Zhilin Han for his help with the calculations related to the interphase layer problem.


  • Interphase layer
  • Spherical inhomogeneity
  • Steigmann-Ogden model
  • Surface effects


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