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.

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.

U2 - 10.1016/j.jappmathmech.2014.09.010

DO - 10.1016/j.jappmathmech.2014.09.010

M3 - статья

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 -