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On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes

  • Roman A. Gerasimov
  • Tatiana O. Petrova
  • Victor A. EremeyevEmail author
  • Andrei V. Maximov
  • Olga G. Maximova
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)

Abstract

Motivating by theory of polymers, in particular, by the models of polymeric brushes we present here the homogenized (continual) two-dimensional (2D) model of surface elasticity. A polymeric brush consists of an system of almost aligned rigid polymeric chains. The interaction between chain links are described through Stockmayer potential, which take into account also dipole-dipole interactions. The presented 2D model can be treated as an highly anisotropic 2D strain gradient elasticity. The surface strain energy contains both first and second derivatives of the surface field of displacements. So it represents an intermediate class of 2D models of the surface elasticity such as Gurtin-Murdoch and Steigmann-Ogden ones.

Notes

Acknowledgements

The author acknowledges financial support from the Russian Science Foundation under the grant “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No. 15-19-10008-P).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Roman A. Gerasimov
    • 1
  • Tatiana O. Petrova
    • 1
  • Victor A. Eremeyev
    • 1
    • 2
    • 3
    Email author
  • Andrei V. Maximov
    • 4
  • Olga G. Maximova
    • 4
  1. 1.Southern Federal UniversityRostov on DonRussia
  2. 2.Faculty of Civil Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  3. 3.Southern Scientific Center of RASciRostov on DonRussia
  4. 4.Cherepovets State UniversityCherepovetsRussia

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