Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2020, Volume 16, Issue 2, Pages 165–176
DOI: https://doi.org/10.21638/11701/spbu10.2020.208
(Mi vspui448)
 

This article is cited in 4 scientific papers (total in 4 papers)

Applied mathematics

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

G. M. Shuvalov, A. B. Vakaeva, D. A. Shamsutdinov, S. A. Kostyrko

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (585 kB) Citations (4)
References:
Abstract: Based on the Gurtin—Murdoch surface/interface elasticity theory, the article investigates the effect of nonlinear terms in the boundary perturbation method on stress concentration near the curvilinear bimaterial interface taking into account plane strain conditions. The authors consider the 2D boundary value problem for the infinite two-component plane under uniaxial tension. The interface domain is assumed to be a negligibly thin layer with the elastic properties differing from those of the bulk materials. Using the boundary perturbation method, the authors determined a semi-analytical solution taking into account non-linear approximations. In order to verify this solution, the corresponding boundary value problem was solved using the finite element method where the interface layer is modelled by the truss elements. It was shown that the effect of the amplitude-to-wavelength ratio of surface undulation on the stress concentration is nonlinear. This should be taken into account even for small perturbations. It was also found that the convergence rate of the derived solution increases with an increase in the relative stiffness coefficient of the bimaterial system and, conversely, decreases with an increase of the amplitude-to-wavelength ratio.
Keywords: bimaterial composites, nanomaterials, interface stress, 2D problem, boundary perturbation method, finite element method, size-effect, interface nano-asperities.
Funding agency Grant number
Russian Foundation for Basic Research 19-71-00062
This work was supported by the Russian Science Foundation (project N 19-71-00062).
Received: April 27, 2020
Accepted: May 28, 2020
Document Type: Article
UDC: 539.4
MSC: 74G10
Language: English
Citation: G. M. Shuvalov, A. B. Vakaeva, D. A. Shamsutdinov, S. A. Kostyrko, “The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 16:2 (2020), 165–176
Citation in format AMSBIB
\Bibitem{ShuVakSha20}
\by G.~M.~Shuvalov, A.~B.~Vakaeva, D.~A.~Shamsutdinov, S.~A.~Kostyrko
\paper The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2020
\vol 16
\issue 2
\pages 165--176
\mathnet{http://mi.mathnet.ru/vspui448}
\crossref{https://doi.org/10.21638/11701/spbu10.2020.208}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    References:15
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