Surface Viscoelasticity and Effective Properties of Materials and Structures
In this paper we discuss the influence of surface viscoelasticity on the effective properties of materials such as effective bending stiffness of plates or shells. Viscoelasticity in the vicinity of the surface can differ from the properties of the bulk material, in general. This difference influences the behavior of nanosized thin elements. In particular, the surface viscoelastic stresses are responsible for the size-depended dissipation of nanosized structures. Extending of the Gurtin-Murdoch model and using the correspondence principle of the linear viscoelasticity we derive the expressions of the stress resultant tensors for shear deformable plates and shells.
KeywordsSurface stresses Surface viscoelasticity Shell Plate Constitutive equations Effective properties
The second author was supported by the DFG with the grant No. AL 341/33-1 and by the RFBR with the grant No. 12-01-00038.
- 2.Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. Adv. Appl. Mech. 42, 1–68 (2008)Google Scholar
- 4.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(1), 52–82 (2011)Google Scholar
- 12.Wang, Z.Q., Zhao, Y.P.: Self-instabilityand bending behaviors of nano plates. Acta Mechanica Solida Sinica 22(6), 630–643 (2009)Google Scholar
- 14.Seoánez, C., Guinea, F., Castro Neto, A.H.: Surface dissipation in nanoelectromechanical systems: unified description with the standard tunneling model and effects of metallic electrodes. Phys. Rev. B 77(12), 125107 (2008)Google Scholar
- 15.Ru, C.Q.: Size effect of dissipative surface stress on quality factor of microbeams. Appl. Phys. Lett. 94, 051905-1–051905-3 (2009)Google Scholar
- 16.Altenbach, H., Eremeyev, V.A., Morozov, N.F.: Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale. Int. J. Eng. Sci. 59, 83–89 (2012)Google Scholar
- 19.Christensen, R.M.: Theory of Viscoelasticity. An Introduction. Academic Press, New York (1971)Google Scholar