Surface effects in an elastic solid with nanosized surface asperities

Research output

20 Citations (Scopus)

Abstract

The effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1–100 nm is investigated. The general two-dimensional prob- lem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin–Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which dif- fer from those of the bulk. The boundary conditions at the curved surface are described by the general- ized Young–Laplace equation. Using a specific approach to the boundary perturbation technique, Goursat–Kolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order appro
Original languageEnglish
Pages (from-to)153-161
JournalInternational Journal of Solids and Structures
Volume96
DOIs
Publication statusPublished - 2016

Fingerprint

Surface Effects
Surface Tension
interfacial tension
Surface tension
curved surfaces
Hypersingular Integral Equation
Complex Potential
Perturbation techniques
Curved Surface
boundary value problems
Perturbation Technique
surface properties
stress distribution
Stress Field
integral equations
One Dimension
Boundary value problems
Integral equations
elastic properties
Surface properties

Cite this

@article{2a2d6831aebf42cb8a8f12c9ad46c8af,
title = "Surface effects in an elastic solid with nanosized surface asperities",
abstract = "The effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1–100 nm is investigated. The general two-dimensional prob- lem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin–Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which dif- fer from those of the bulk. The boundary conditions at the curved surface are described by the general- ized Young–Laplace equation. Using a specific approach to the boundary perturbation technique, Goursat–Kolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order appro",
keywords = "Surface asperities, Surface stress, Surface tension, Stress concentration, Size effect",
author = "M.A. Grekov and S.A. Kostyrko",
year = "2016",
doi = "10.1016/j.ijsolstr.2016.06.013",
language = "English",
volume = "96",
pages = "153--161",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier",

}

TY - JOUR

T1 - Surface effects in an elastic solid with nanosized surface asperities

AU - Grekov, M.A.

AU - Kostyrko, S.A.

PY - 2016

Y1 - 2016

N2 - The effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1–100 nm is investigated. The general two-dimensional prob- lem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin–Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which dif- fer from those of the bulk. The boundary conditions at the curved surface are described by the general- ized Young–Laplace equation. Using a specific approach to the boundary perturbation technique, Goursat–Kolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order appro

AB - The effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1–100 nm is investigated. The general two-dimensional prob- lem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin–Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which dif- fer from those of the bulk. The boundary conditions at the curved surface are described by the general- ized Young–Laplace equation. Using a specific approach to the boundary perturbation technique, Goursat–Kolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order appro

KW - Surface asperities

KW - Surface stress

KW - Surface tension

KW - Stress concentration

KW - Size effect

U2 - 10.1016/j.ijsolstr.2016.06.013

DO - 10.1016/j.ijsolstr.2016.06.013

M3 - Article

VL - 96

SP - 153

EP - 161

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -