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The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole. / Grekov, M.A.; Yazovskaya, A.A.

In: Journal of Applied Mathematics and Mechanics, Vol. 78, No. 2, 2014, p. 172-180.

Research output: Contribution to journal › Article › peer-review

Harvard

Grekov, MA & Yazovskaya, AA 2014, 'The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole', Journal of Applied Mathematics and Mechanics, vol. 78, no. 2, pp. 172-180. https://doi.org/10.1016/j.jappmathmech.2014.07.010, https://doi.org/10.1016/j.jappmathmech.2014.09.010

APA

Grekov, M. A., & Yazovskaya, A. A. (2014). The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole. Journal of Applied Mathematics and Mechanics, 78(2), 172-180. https://doi.org/10.1016/j.jappmathmech.2014.07.010, https://doi.org/10.1016/j.jappmathmech.2014.09.010

Vancouver

Grekov MA, Yazovskaya AA. The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole. Journal of Applied Mathematics and Mechanics. 2014;78(2):172-180. https://doi.org/10.1016/j.jappmathmech.2014.07.010, https://doi.org/10.1016/j.jappmathmech.2014.09.010

Author

Grekov, M.A. ; Yazovskaya, A.A. / The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole. In: Journal of Applied Mathematics and Mechanics. 2014 ; Vol. 78, No. 2. pp. 172-180.

BibTeX

@article{f34e49a623f34a5b832d5a358e3661bf,
title = "The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole",
abstract = "The deformation of an elastic plane with an elliptic hole in a uniform stress field is considered, taking into account the surface elasticity and the residual surface tension. The solution of the problem, based on the use of the linearized Gurtin-Murdoch surface elasticity relations and the complex Goursat-Kolosov potentials, is reduced to a singular integrodifferential equation. Using the example of a circular hole, for which an exact solution of the equation is obtained in closed form, the effect of the residual surface tension and the surface elasticity on the stress state close to and on the boundary of a nanohole is analysed for uniaxial tension. It is shown that the effect of the residual surface stress and the surface tension, due to deformation of the body, depends on the elastic properties of the surface, the value of the stretching load and the dimensions of the hole.",
author = "M.A. Grekov and A.A. Yazovskaya",
note = "Funding Information: This research was supported by the Russian Foundation for Basic Research (11-01-00230) and the St Petersburg State University (9.37.129.2011). Publisher Copyright: {\textcopyright} 2014 Elsevier Ltd. All rights reserved. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",
year = "2014",
doi = "10.1016/j.jappmathmech.2014.07.010",
language = "English",
volume = "78",
pages = "172--180",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole

AU - Grekov, M.A.

AU - Yazovskaya, A.A.

N1 - Funding Information: This research was supported by the Russian Foundation for Basic Research (11-01-00230) and the St Petersburg State University (9.37.129.2011). Publisher Copyright: © 2014 Elsevier Ltd. All rights reserved. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2014

Y1 - 2014

N2 - The deformation of an elastic plane with an elliptic hole in a uniform stress field is considered, taking into account the surface elasticity and the residual surface tension. The solution of the problem, based on the use of the linearized Gurtin-Murdoch surface elasticity relations and the complex Goursat-Kolosov potentials, is reduced to a singular integrodifferential equation. Using the example of a circular hole, for which an exact solution of the equation is obtained in closed form, the effect of the residual surface tension and the surface elasticity on the stress state close to and on the boundary of a nanohole is analysed for uniaxial tension. It is shown that the effect of the residual surface stress and the surface tension, due to deformation of the body, depends on the elastic properties of the surface, the value of the stretching load and the dimensions of the hole.

AB - The deformation of an elastic plane with an elliptic hole in a uniform stress field is considered, taking into account the surface elasticity and the residual surface tension. The solution of the problem, based on the use of the linearized Gurtin-Murdoch surface elasticity relations and the complex Goursat-Kolosov potentials, is reduced to a singular integrodifferential equation. Using the example of a circular hole, for which an exact solution of the equation is obtained in closed form, the effect of the residual surface tension and the surface elasticity on the stress state close to and on the boundary of a nanohole is analysed for uniaxial tension. It is shown that the effect of the residual surface stress and the surface tension, due to deformation of the body, depends on the elastic properties of the surface, the value of the stretching load and the dimensions of the hole.

UR - http://www.scopus.com/inward/record.url?scp=84944443405&partnerID=8YFLogxK

U2 - 10.1016/j.jappmathmech.2014.07.010

DO - 10.1016/j.jappmathmech.2014.07.010

M3 - Article

VL - 78

SP - 172

EP - 180

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 2

ER -

ID: 5720078