TY - JOUR

T1 - The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

AU - Shuvalov, G. M.

AU - Vakaeva, A. B.

AU - Shamsutdinov, D. A.

AU - Kostyrko, S. A.

N1 - Funding Information: ∗ This work was supported by the Russian Science Foundation (project N 19-71-00062). ©c Санкт-Петербу ргский госу дарственный у ниверситет, 2020 Publisher Copyright: © Санкт-Петербургский государственный университет Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - 2D problem

KW - Bimaterial composites

KW - Boundary perturbation method

KW - Finite element method

KW - Interface nano-asperities

KW - Interface stress

KW - Nanomaterials

KW - Size-effect

UR - http://www.scopus.com/inward/record.url?scp=85091236270&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3c3452e0-84f4-3621-8696-cb9cb832ada1/

U2 - 10.21638/11701/SPBU10.2020.208

DO - 10.21638/11701/SPBU10.2020.208

M3 - Article

AN - SCOPUS:85091236270

VL - 16

SP - 165

EP - 176

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 2

ER -