Buckling of an elastic plate due to surface-attached thin films with intrinsic stresses

  • Zhu, J. (College of Mechanical Engineering, Zhejiang University of Technology) ;
  • Yang, J.S. (Department of Engineering Mechanics, University of Nebraska) ;
  • Ru, C.Q. (Department of Mechanical Engineering, University of Alberta)
  • Received : 2014.04.13
  • Accepted : 2014.06.20
  • Published : 2014.10.10


We analyze the buckling of a thin elastic plate due to intrinsic stresses in thin films attached to the surfaces of the plate. In the case of cylindrical buckling, it is shown that for a plate with clamped edges compressive intrinsic film stresses can cause flexural buckling of the plate, while tensile intrinsic film stresses cannot. For a plate with free edges, film intrinsic stresses, compressive or tensile, cannot cause buckling.


  1. Cuenot, S., Fretigny, C., Champagne, S.D. and Nysten, B. (2004), "Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy", Phys. Rev. B, 69, 165410.
  2. Dong, C.Y. and Pan, E. (2011), "Boundary element analysis of nanoinhomogeneities of arbitrary shapes with surface and interface effects", Eng. Anal. Bound. Elem., 35, 996-1002.
  3. Guo, J.G. and Zhao, Y.P. (2007), "The size-dependent bending elastic properties of nanobeams with surface effects", Nanotechnology, 18, 295701.
  4. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. An., 57(4), 291-323.
  5. Kornev, K.G. and Srolovitz, D.J. (2004), "Surface stress-driven instability of a free film", Appl. Phys. Lett., 85(13), 2487-2489.
  6. Mi, C., Jun, S., Kouris, D.A. and Kim, S.Y. (2008), "Atomistic calculations of interface elastic properties in noncoherent metallic bilayers", Phys. Rev. B, 77, 075425
  7. Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11, 139-147.
  8. Liang, L.H., Li, J.C. and Jiang, Q. (2002), "Size-dependent elastic modulus of Cu and Au thin films", Solid State Commun., 121, 453-455.
  9. Lu, P., He, L.H., Lee, H.P. and Lu, C. (2006), "Thin plate theory including surface effects", Int. J. Solids Struct., 43(16), 4631-4647.
  10. Shenoy, V.B. (2005), "Atomistic calculations of elastic properties of metallic fcc crystal surfaces", Phys. Rev. B, 71, 094101.
  11. Streitz, F.H., Cammarata, R.C. and Sieradzki, K. (1994), "Surface-stress effects on elasticproperties. I. Thin metal films", Phys. Rev. B, 49, 10699
  12. Tian, L. and Rajapakse, R.K.N.D. (2007), "Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity", In. J. Solids Struct., 44(22), 7988-8005.
  13. Tiersten, H.F., Sinha, B.K. and Meeker, T.R. (1981), "Intrinsic stress in thin films deposited on anisotropic substrates and its influence on the natural frequencies of piezoelectric resonators", J. Appl. Phys., 52(9), 5614-5624.
  14. Villain, P., Beauchamp, P. K., Badwi, F., Goudeau, P. and Renault, P.O. (2004), "Atomistic calculation of size effects on elastic coefficients in nanometre-sized tungsten layers and wires", Scr. Mater., 50(9), 1247-1251.
  15. Wang, Z.Q. and Zhao, Y.P. (2009), "Self-instability and bending behaviors of nano plates", Acta Mech. Solida Sin., 22(6), 630-643.
  16. Yang, F.Q. (2004), "Size-dependent effective modulus of elastic composite materials: spherical nanocavities at dilute concentrations", J. Appl. Phys., 95(7), 3516-3520.