Multiple interacting circular nano-inhomogeneities with surface/interface effects

Sofia G. Mogilevskaya, Steven L. Crouch, Henryk K. Stolarski

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A two-dimensional problem of multiple interacting circular nano-inhomogeneities or/and nano-pores is considered. The analysis is based on the Gurtin and Murdoch model [Gurtin, M.E., Murdoch, A.I., 1975. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291-323.] in which the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces that possess their own mechanical properties and surface tension. The precise component forms of Gurtin and Murdoch's three-dimensional equations are derived for interfaces of arbitrary shape to provide a basis for critical review of various modifications used in the literature. The two-dimensional specification of these equations is considered and their representation in terms of complex variables is provided. A semi-analytical method is proposed to solve the problem. Solutions to several example problems are presented to: (i) examine the difference between the results obtained with the original and modified Gurtin and Murdoch's equations, (ii) compare the results obtained using Gurtin and Murdoch's model and those for a problem of nano-inhomogeneities with thin membrane-type interphase layers, and (iii) demonstrate the effectiveness of the approach in solving problems with multiple nano-inhomogeneities.

Original languageEnglish (US)
Pages (from-to)2298-2327
Number of pages30
JournalJournal of the Mechanics and Physics of Solids
Issue number6
StatePublished - Jun 2008


  • Boundary integral equations
  • Gurtin and Murdoch model
  • Nano-inhomogeneity
  • Surface elasticity
  • Surface tension


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