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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Bažant, Z.P.: Size effect. Int. J. Solids Struct. 37(1–2), 69–80 (2000)
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)
Guo, J.G., Zhao, Y.P.: The size-dependent elastic properties of nanofilms with surface effects. J. Appl. Phys. 98(7), 074306–074311 (2005)
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)
Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)
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)
Huang, Z., Wang, J.: A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mechanica 182, 195–210 (2006)
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)
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)
Lebedev, L.P., Cloud, M.J., Eremeyev, V.A.: Tensor Analysis with Applications in Mechanics. World Scientific, New Jersey (2010)
Lurie, A.I.: Nonlinear Theory of Elasticity. North-Holland, Amsterdam (1990)
Ogden, R.W.: Non-linear Elastic Deformations. Ellis Horwood, Chichester (1984)
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)
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)
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)
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)
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)
Acknowledgments
The second author was supported by the DFG grant No. AL 341/33-1 and by the RFBR with the grant No. 12-01-00038.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Altenbach, H., Eremeyev, V.A., Morozov, N.F. (2013). On the Influence of Residual Surface Stresses on the Properties of Structures at the Nanoscale. In: Altenbach, H., Morozov, N. (eds) Surface Effects in Solid Mechanics. Advanced Structured Materials, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35783-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-35783-1_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35782-4
Online ISBN: 978-3-642-35783-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)