Abstract
This paper studies surface instability of a coated semi-infinite linear elastic body interacting with another flat rigid body through surface van der Waals (vdW) forces under plane strain conditions. The emphasis is on the effect of the surface coating layer on the wavelength of surface wrinkling. It is shown that the surface of the coated elastic half-plane is always unstable even in the presence of a very stiff coating layer. However, the numerical results show that the stiff coating layer has a significant effect on the wavelength of the surface instability mode and can effectively prevent the surface from short-wavelength wrinkling. In particular, the surface tangential displacement associated with the surface instability vanishes when the elastic half-plane is incompressible. In this case, the in-plane rigidity of the coating layer has no effect on surface instability while the bending stiffness of the coating layer has an effect on the wave-length of the surface instability mode. Furthermore, the Poisson’s ratio of elastic half-plane has a significant role in the surface instability and the associated wave-length.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Israelachvili, J.: Intermolecular and Surface Forces, 2nd edn. Academic, San Diego, CA (1992)
Johnson, K.L.: Continuum mechanics modeling of adhesion and friction. Langmuir 12, 4510–4513 (1996)
Monch, W., Herminghaus, S.: Elastic instability of rubber films between solid bodies. Europhys. Lett. 53, 525–531 (2001)
Shenoy, V., Sharma, A.: Pattern formation in a thin solid film with interactions. Phys. Rev. Lett. 86, 119–122 (2001)
Nowinski, J.L.: Surface instability of a half-space under highly two-dimensional compression. J. Franklin Inst. 228, 367–376 (1969)
Andreussi, F., Gurtin, M.E.: On the wrinkling of a free surface. J. Appl. Phys. 48, 3798–3799 (1977)
Gent, A.N., Cho, I.S.: Surface instability in compressed or bent rubber blocks. Rubber Chem. Technol. 72, 253–262 (1999)
Srolovitz, D.J.: On the stability of surfaces of stressed solids. Acta Metall. 37, 621–624 (1989)
Ru, C.Q.: Surface instability of a semi-infinite elastic body under surface van der Waals forces. J. Appl. Mech. 71, 138–140 (2004)
Fried, E., Todres, R.E.: Mind the gap: the shape of the free surface of a rubber-like material in proximity to a rigid contactor. J. Elast. 80, 97–151 (2006)
Yoon, J., Ru, C.Q., Mioduchowski, A.: Surface instability of a bilayer elastic film due to surface van der Waal forces. J. Appl. Phys. 98, 113503-1−113503-11 (2005)
Hu, S.M.: Stress-related problems in silicon technology. J. Appl. Phys. 70, R53–R80 (1991)
Gioia, G., Ortiz, M.: Compressed failure of thin films. Adv. Appl. Mech. 33, 119–192 (1997)
Ogden, R.W., Steigmann, D.J.: Plane strain dynamics of elastic solids with intrinsic boundary elasticity, with application to surface wave propagation. J. Mech. Phys. Solids 50, 1869–1896 (2002)
Mansfield, E.H.: Neutral holes in plane sheet-reinforced holes which elastically equivalent to the uncut sheet. Q. J. Mech. Appl. Math. VI, 370–378 (1953)
Radok, J.R.M.: Problems of plane elasticity for reinforced boundaries. J. Appl. Mech. (ASME), 246–254 (1955)
Arutiunian, N.K., Mikhitarian, S.M.: Contact problem of pressing a stamp into an elastic half-plane with a thin reinforcing covering. J. Appl. Math. Mech. (PMM) 39, 857–875 (1975)
Richard, R., Bjorkman, G.S.: Neutral holes: theory and design. J. Eng. Mech. (ASCE) 108, 945–960 (1982)
Shield, T.W., Kim, K.S.: Beam theory models for thin film segments cohesively bounded to an elastic half-space. Int. J. Solids Struct. 29, 1085–1103 (1992)
Schiavone, P., Ru, C.Q.: Integral equation methods in plane-strain elasticity with boundary reinforcement. Proc. R. Soc. Lond., A Math. Phys. Sci. 454, 2223–2242 (1998)
Yoon, J., Ru, C.Q., Mioduchowski, A.: Effect of a thin surface coating layer on thermal stresses within an elastic half-plane. Acta Mech. 1619–6937 (2005) (Online)
Schaffer, E., Albrecht, T.T., Russell, T.P., Steiner, U.: Electrically induced structure formation and pattern transfer. Nature (Lond.) 403, 874–877 (2000)
England, A.E.: Complex-variable Methods in Elasticity. Wiley, London (1971)
Pethica, J.B., Sutton, A.P.: On the stability of a tip and flat at very small separation. J. Vac. Sci. Technol., A. 6, 2490–2494 (1988)
Qian, D., Wagner, G.J., Liu, W.K., Yu, M.F., Ruoff, R.S.: Mechanics of carbon nanotubes. Appl. Mech. Rev. 55, 495–533 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
C. Q. Ru is on leave from the University of Alberta, Edmonton, T6G. 2G8, Canada.
Rights and permissions
About this article
Cite this article
Qian, H., Xu, K.Y. & Ru, C.Q. Surface Forces Driven Wrinkling of an Elastic Half-Space Coated with a Thin Stiff Surface Layer. J Elasticity 86, 205–219 (2007). https://doi.org/10.1007/s10659-006-9083-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-006-9083-z