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Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials pp 153–161Cite as

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

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Part of the book series: Advanced Structured Materials ((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.

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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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Authors and Affiliations

  1. Southern Federal University, Milchakova str. 8a, 344090, Rostov on Don, Russia

    Roman A. Gerasimov, Tatiana O. Petrova & Victor A. Eremeyev

  2. Faculty of Civil Environmental Engineering, Gdańsk University of Technology, ul. Gabriela Narutowicza 11/12, 80-233, Gdańsk, Poland

    Victor A. Eremeyev

  3. Southern Scientific Center of RASci, Chekhova str. 41, 344006, Rostov on Don, Russia

    Victor A. Eremeyev

  4. Cherepovets State University, 5 Lunacharskii Av, 162600, Cherepovets, Russia

    Andrei V. Maximov & Olga G. Maximova

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  1. Roman A. Gerasimov
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  2. Tatiana O. Petrova
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  3. Victor A. Eremeyev
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  5. Olga G. Maximova
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Corresponding author

Correspondence to Victor A. Eremeyev .

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Editors and Affiliations

  1. Institute for Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, Russia

    Mezhlum A. Sumbatyan

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Gerasimov, R.A., Petrova, T.O., Eremeyev, V.A., Maximov, A.V., Maximova, O.G. (2019). On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes. In: Sumbatyan, M. (eds) Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials. Advanced Structured Materials, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-17470-5_11

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