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

Roman Gerasimov; Tatiana Petrova; Victor Eremeev; Andrei Maximov; Olga Maximova

doi:10.1007/978-3-030-17470-5_11

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

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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Authors (5)

Roman Gerasimov Dr
Tatiana Petrova Dr
Victor Eremeev prof. dr hab.
Andrei Maximov Dr Prof
Olga Maximova Dr Prof

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Category:: Monographic publication
Type:: rozdział, artykuł w książce - dziele zbiorowym /podręczniku w języku o zasięgu międzynarodowym
Title of issue:: Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials strony 153 - 161
Language:: English
Publication year:: 2019
Bibliographic description:: Gerasimov R., Petrova T., Eremeev V., Maximov A., Maximova O.: On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes// Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials:Theoretical and Experimental Methods/ Cham: Springer, 2019, s.153-161
DOI:: Digital Object Identifier (open in new tab) 10.1007/978-3-030-17470-5_11
Verified by:: Gdańsk University of Technology