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Surface instability of orthotropic films under surface van der Waals forces

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Abstract

We investigate the surface instability of an orthotropic thin elastic film interacting with another flat rigid body through van der Waals forces by means of linear stability analysis. In the obtained dispersion relation, the normalized interaction coefficient can be completely determined by the normalized wavenumber, the normalized surface energy and other two dimensionless material parameters characterizing the orthotropic elasticity of the film. The influence of these two material parameters and surface energy on the critical bifurcation mode and the critical interaction coefficient is probed in detail. The dispersion relation is also obtained for degenerate orthotropic films. An effective method based on transfer matrix is employed to derive the dispersion relations for a multilayered orthotropic elastic film interacting with a rigid contactor and interacting with another multilayered orthotropic elastic film, and also to obtain the critical interaction coefficient for a simply supported mono-layered orthotropic plate attracted by a rigid flat. Some interesting phenomena are observed for a bilayered orthotropic film, for two interacting mono-layered orthotropic films and for an orthotropic plate.

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References

  1. 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 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. He, L.H., Jiang, J.: Transient mechanical response of laminated elastic strips with viscous interfaces in cylindrical bending. Comput. Sci. Technol. 63, 821–828 (2003)

    Article  Google Scholar 

  3. Huang, S.Q., Li, Q.Y., Feng, X.Q., Yu, S.W.: Pattern instability of a soft elastic thin film under van der Waals forces. Mech. Mater. 38, 88–99 (2006)

    Article  Google Scholar 

  4. Li, B., Zhao, H.P., Feng, X.Q.: Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction. J. Mech. Phys. Solids 59, 610–624 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pan, X.H., Huang, S.Q., Yu, S.W., Feng, X.Q.: Interfacial slippage effect on the surface instability of a thin elastic film under van der Waals force. J. Phys. D: Appl. Phys. 42, 055302 (2009)

    Article  Google Scholar 

  6. Ru, C.Q.: Surface wrinkling of two mutually attracting elastic thin films due to van der Waals forces. J. Appl. Phys. 90, 6098–6104 (2001)

    Article  Google Scholar 

  7. Ru, C.Q.: Surface instability of an elastic thin film interacting with a suspended elastic plate. ASME J. Appl. Mech. 69, 97–103 (2002)

    Article  MATH  Google Scholar 

  8. Ru, C.Q.: Surface instability of a semi-infinite elastic body under van der Waals forces. ASME J. Appl. Mech. 71, 138–140 (2004)

    Article  MATH  Google Scholar 

  9. Shenoy, V., Sharma, A.: Pattern formation in a thin solid film with interactions. Phys. Rev. Lett. 86, 119–122 (2001)

    Article  Google Scholar 

  10. Shenoy, V., Sharma, A.: Stability of a thin elastic film interacting with a contactor. J. Mech. Phys. Solids 50, 1155–1173 (2002)

    Article  MATH  Google Scholar 

  11. Suo, Z.G.: Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. R. Soc. Lond. A 427, 331–358 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tomar, G., Sharma, A.: Contact instabilities of anisotropic and inhomogeneous soft elastic films. Phys. Rev. E 85, 021603 (2012)

    Article  Google Scholar 

  13. Wang, G.F., Schiavone, P., Ru, C.Q.: Surface instability of a semi-infinite harmonic solid under van der Waals attraction. Acta Mech. 180, 1–10 (2005)

    Article  MATH  Google Scholar 

  14. Wang, X.: Surface instability of a semi-infinite anisotropic elastic body under surface van der Waals forces. Mech. Res. Commun. 35, 181–186 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, X., **g, R.: Surface instability of an imperfectly bonded thin elastic film under surface van der Waals forces. Z. Angew. Math. Phys. 68(1), 1–20 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, X., Sudak, L.J., Pan, E.: Pattern instability of functionally graded and layered elastic films under van der Waals forces. Acta Mech. 198, 65–86 (2008)

    Article  MATH  Google Scholar 

  17. Yoon, J., Ru, C.Q., Mioduchowski, A.: Surface instability of a bilayer elastic film due to surface van der Waals forces. J. Appl. Phys. 98, 113503_1–113503_11 (2005)

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang & Shuxiang Li

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  1. Xu Wang
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  2. Shuxiang Li
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Correspondence to Xu Wang.

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Wang, X., Li, S. Surface instability of orthotropic films under surface van der Waals forces. Z. Angew. Math. Phys. 68, 85 (2017). https://doi.org/10.1007/s00033-017-0831-7

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  • DOI: https://doi.org/10.1007/s00033-017-0831-7

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