Surface Effects in Solid Mechanics pp 21-32

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 30) | Cite as

On the Influence of Residual Surface Stresses on the Properties of Structures at the Nanoscale

  • Holm Altenbach
  • Victor A. Eremeyev
  • Nikita F. Morozov
Chapter

Abstract

We discuss the influence of residual surface stresses on the effective (apparent) properties of materials at the nanoscale such as the stiffness of rods. The interest to the investigation of the surface effects is recently grown with respect to progress in nanotechnologies. The surface and interface effects play an important role for nanofilms, nanocomposites, nanoporous materials, etc. Here we consider the Gurtin–Murdoch model of surface elasticity. With the help of the simple problem of uniaxial tension of a rod with residual surface stresses we analyze the behavior of the rod under tension and present the effective stiffness.

References

  1. 1.
    Altenbach, H., Eremeyev, V.A., Lebedev, L.P.: On the spectrum and stiffness of an elastic body with surface stresses. ZAMM 91(9), 699–710 (2011)Google Scholar
  2. 2.
    Bažant, Z.P.: Size effect. Int. J. Solids Struct. 37(1–2), 69–80 (2000)Google Scholar
  3. 3.
    Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. In: Advances in Applied Mechanics, vol. 42, pp. 1–68. Elsevier, San Diego (2008)Google Scholar
  4. 4.
    Guo, J.G., Zhao, Y.P.: The size-dependent elastic properties of nanofilms with surface effects. J. Appl. Phys. 98(7), 074306–074311 (2005)Google Scholar
  5. 5.
    Gurtin, M.E., Markenscoff, X., Thurston, R.N.: Effect of surface stress on natural frequency of thin crystals. Appl. Phys. Lett. 29(9), 529–530 (1976)Google Scholar
  6. 6.
    Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)Google Scholar
  7. 7.
    Huang, Z., Sun, L.: Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis. Acta Mechanica 190, 151–163 (2007)Google Scholar
  8. 8.
    Huang, Z., Wang, J.: A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mechanica 182, 195–210 (2006)Google Scholar
  9. 9.
    Huang, Z., Wang, J.: Micromechanics of nanocomposites with interface energy effect. In: Handbook on Micromechanics and Nanomechanics, p. 48. Pan Stanford Publishing, Singapore (2012) (in print)Google Scholar
  10. 10.
    Lagowski, J., Gatos, H.C., Sproles, E.S.: Surface stress and normal mode of vibration of thin crystals: GaAs. Appl. Phys. Lett. 26(9), 493–495 (1975)Google Scholar
  11. 11.
    Lebedev, L.P., Cloud, M.J., Eremeyev, V.A.: Tensor Analysis with Applications in Mechanics. World Scientific, New Jersey (2010)Google Scholar
  12. 12.
    Lurie, A.I.: Nonlinear Theory of Elasticity. North-Holland, Amsterdam (1990)Google Scholar
  13. 13.
    Ogden, R.W.: Non-linear Elastic Deformations. Ellis Horwood, Chichester (1984)Google Scholar
  14. 14.
    Wang, G.F., Feng, X.Q.: Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl. Phys. Lett. 90(23), 231904 (2007)Google Scholar
  15. 15.
    Wang, J., Duan, H.L., Huang, Z.P., Karihaloo, B.L.: A scaling law for properties of nano-structured materials. Proc. Royal Soc. Lond. A 462(2069), 1355–1363 (2006)Google Scholar
  16. 16.
    Wang, J., Huang, Z., Duan, H., Yu, S., Feng, X., Wang, G., Zhang, W., Wang, T.: Surface stress effect in mechanics of nanostructured materials. Acta Mechanica Solida Sinica 24, 52–82 (2011)Google Scholar
  17. 17.
    Wang, Z.Q., Zhao, Y.P., Huang, Z.P.: The effects of surface tension on the elastic properties of nano structures. Int. J. Eng. Sci. 48(2), 140–150 (2010)Google Scholar
  18. 18.
    Zhu, H.X., Wang, J.X., Karihaloo, B.L.: Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms. J. Mech. Mater. Struct. 4(3), 589–604 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Holm Altenbach
    • 1
  • Victor A. Eremeyev
    • 1
    • 2
  • Nikita F. Morozov
    • 3
  1. 1.Institut für MechanikFakultät für Maschinenbau, Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.South Scientific Center of RASci & South Federal UniversityRostov on DonRussia
  3. 3.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations