Effect of Surface Stress on the Deformation around a Nanosized Elliptical Hole: a Finite Element Study
When the characteristic length of an elastic solid is
down to the nanometer level, its deformation behavior becomes size
dependent. Surface energy /surface stress have recently been applied
to explain such dependency. In this paper, the effect of
strain-independent surface stress on the deformation of an isotropic
elastic solid containing a nanosized elliptical hole is studied by the
finite element method. Two loading cases are considered, in the first
case, hoop stress along the rim of the elliptical hole induced by pure
surface stress is studied, in the second case, hoop stress around the
elliptical opening under combined remote tension and surface stress is
investigated. It has been shown that positive surface stress induces
compressive hoop stress along the hole, and negative surface stress has
opposite effect, maximum hoop stress occurs near the major semi-axes
of the ellipse. Under combined loading of remote tension and surface
stress, stress concentration around the hole can be either intensified or
weakened depending on the sign of the surface stress.
[1] M. E. Gurtin, and A. I. Murdoch, "A continuum theory of elastic material
surfaces," Arch. Ration. Mech. Anal., vol. 57, pp. 291-323, 1975.
[2] M. E. Gurtin, and A. I. Murdoch, "Surface stress in solids," Int. J. Solids
and Struct., vol.14, pp. 431-440, 1978.
[3] R. E. Miller, and V. Shenoy, "Size-dependent elastic properties of
nanosized structural elements," Nanotechnology, vol. 11, pp. 139-147,
2002.
[4] P. Sharma, S. Ganti, and N. Bhate, "Effect of surfaces on the
size-dependent elastic state of nano-imhomogeneities," Applied Physics
Letters, vol. 82, pp.535-537, 2003.
[5] P. Sharma P, and S. Ganti, "Size-dependent Eshelby's tensor for
embedded nano-inclusions incorporating surface/interface energies," J.
Applied Mechanics, vol. 71, pp. 663-671, 2004.
[6] F. Yang, "Size-dependent effective modulus of elastic composite
materials: spherical nanocavities at dilute concentrations," J. Applied
Physics, vol. 95, pp. 3516-3520, 2004.
[7] G. F. Wang, and T. J. Wang, "Deformation around a nanosized elliptical
hole with surface effect," Applied Physics Letters, vol. 89: pp.
161901-161903, 2006.
[8] L. Tian L, and R. K. N. D. Rajapakse, "Analytical solution for
size-dependent elastic field of a nanoscale circular inhomogeneity," J.
Applied Mechanics, vol. 74, pp. 568-574, 2007.
[9] L. Tian L, and R. K. N. D. Rajapakse, "Elastic field of an isotropic matrix
with a nanoscale elliptical imhomogeneity," Int. J. Solids Struct., vol. 44,
pp. 7988-8005, 2007.
[10] Z. Y. Ou, G. F. Wang, and T. J. Wang, "Effect of residual surface tension
on the stress concentration around a nanosized spheroidal cavity," Int. J.
Engrg. Sci., vol. 46, pp. 475-485, 2008.
[11] H. L. Duan, J. Wang, Z. P. Huang, and B. L. Karihaloo, "Size-dependent
effective elastic constants of solids containing nano-imhomogeneities
with interface stress," J. Mech. Phys. Solids, vol. 53, pp. 1574-1596, 2005.
[12] H. L. Duan, J. Wang, B. L. Karihaloo, and Z. P. Huang, "Nanoporous
materials can be made stiffer than non-porous counterparts by surface
modification," Acta Mater., vol. 54, pp. 2983-2990, 2006.
[13] T. Chen, G. J. Dvorak, and C. C. Yu, "Solids containing spherical
nano-inclusions with interface stresses: effective properties and
thermal-mechanical connections," Int. J. Solids Struct., vol. 44, pp.
941-955, 2007.
[14] W. Gao, S. W. Yu, and G. Y. Huang, " Finite element characterization of
the size-dependent mechanical behavior in nanosystems,"
Nanotechnology, vol. 17, pp. 1118-1122, 2006,
[15] L. Tian, and R. K. N. D. Rajapakse, " Finite element modeling of
nanoscale inhomogeneities in an elastic matrix," Computational
Materials Science, vol. 41, pp. 44-53, 2007.
[16] R. C. Cammarata, "Surface and interface stress effects in thin film," Prog.
Surf. Sci., vol. 46, pp. 1-38, 1994.
[1] M. E. Gurtin, and A. I. Murdoch, "A continuum theory of elastic material
surfaces," Arch. Ration. Mech. Anal., vol. 57, pp. 291-323, 1975.
[2] M. E. Gurtin, and A. I. Murdoch, "Surface stress in solids," Int. J. Solids
and Struct., vol.14, pp. 431-440, 1978.
[3] R. E. Miller, and V. Shenoy, "Size-dependent elastic properties of
nanosized structural elements," Nanotechnology, vol. 11, pp. 139-147,
2002.
[4] P. Sharma, S. Ganti, and N. Bhate, "Effect of surfaces on the
size-dependent elastic state of nano-imhomogeneities," Applied Physics
Letters, vol. 82, pp.535-537, 2003.
[5] P. Sharma P, and S. Ganti, "Size-dependent Eshelby's tensor for
embedded nano-inclusions incorporating surface/interface energies," J.
Applied Mechanics, vol. 71, pp. 663-671, 2004.
[6] F. Yang, "Size-dependent effective modulus of elastic composite
materials: spherical nanocavities at dilute concentrations," J. Applied
Physics, vol. 95, pp. 3516-3520, 2004.
[7] G. F. Wang, and T. J. Wang, "Deformation around a nanosized elliptical
hole with surface effect," Applied Physics Letters, vol. 89: pp.
161901-161903, 2006.
[8] L. Tian L, and R. K. N. D. Rajapakse, "Analytical solution for
size-dependent elastic field of a nanoscale circular inhomogeneity," J.
Applied Mechanics, vol. 74, pp. 568-574, 2007.
[9] L. Tian L, and R. K. N. D. Rajapakse, "Elastic field of an isotropic matrix
with a nanoscale elliptical imhomogeneity," Int. J. Solids Struct., vol. 44,
pp. 7988-8005, 2007.
[10] Z. Y. Ou, G. F. Wang, and T. J. Wang, "Effect of residual surface tension
on the stress concentration around a nanosized spheroidal cavity," Int. J.
Engrg. Sci., vol. 46, pp. 475-485, 2008.
[11] H. L. Duan, J. Wang, Z. P. Huang, and B. L. Karihaloo, "Size-dependent
effective elastic constants of solids containing nano-imhomogeneities
with interface stress," J. Mech. Phys. Solids, vol. 53, pp. 1574-1596, 2005.
[12] H. L. Duan, J. Wang, B. L. Karihaloo, and Z. P. Huang, "Nanoporous
materials can be made stiffer than non-porous counterparts by surface
modification," Acta Mater., vol. 54, pp. 2983-2990, 2006.
[13] T. Chen, G. J. Dvorak, and C. C. Yu, "Solids containing spherical
nano-inclusions with interface stresses: effective properties and
thermal-mechanical connections," Int. J. Solids Struct., vol. 44, pp.
941-955, 2007.
[14] W. Gao, S. W. Yu, and G. Y. Huang, " Finite element characterization of
the size-dependent mechanical behavior in nanosystems,"
Nanotechnology, vol. 17, pp. 1118-1122, 2006,
[15] L. Tian, and R. K. N. D. Rajapakse, " Finite element modeling of
nanoscale inhomogeneities in an elastic matrix," Computational
Materials Science, vol. 41, pp. 44-53, 2007.
[16] R. C. Cammarata, "Surface and interface stress effects in thin film," Prog.
Surf. Sci., vol. 46, pp. 1-38, 1994.
@article{"International Journal of Architectural, Civil and Construction Sciences:62989", author = "Weifeng Wang and Xianwei Zeng and Jianping Ding", title = "Effect of Surface Stress on the Deformation around a Nanosized Elliptical Hole: a Finite Element Study", abstract = "When the characteristic length of an elastic solid is
down to the nanometer level, its deformation behavior becomes size
dependent. Surface energy /surface stress have recently been applied
to explain such dependency. In this paper, the effect of
strain-independent surface stress on the deformation of an isotropic
elastic solid containing a nanosized elliptical hole is studied by the
finite element method. Two loading cases are considered, in the first
case, hoop stress along the rim of the elliptical hole induced by pure
surface stress is studied, in the second case, hoop stress around the
elliptical opening under combined remote tension and surface stress is
investigated. It has been shown that positive surface stress induces
compressive hoop stress along the hole, and negative surface stress has
opposite effect, maximum hoop stress occurs near the major semi-axes
of the ellipse. Under combined loading of remote tension and surface
stress, stress concentration around the hole can be either intensified or
weakened depending on the sign of the surface stress.", keywords = "Surface stress, finite element method, stress
concentration, nanosized elliptical hole", volume = "4", number = "10", pages = "338-5", }