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Effect of Surface Stress on the Deformation around a Nanosized Elliptical Hole: a Finite Element Study

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding


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

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[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.