Skip to main content
Log in

Adhesive contact problem of axisymmetric miniature circular plates with central rigid bump

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Huston,M.R., Maboudian,R. and Howe,R.T., Ammonium fluoride anti-stictiontreatments for poly-silion microstructure, Proceedings of the 8-th International Conference on Solid-State and Actuators, Transducers’95, Stockholm, Sweden, 1995, 210–213.

  2. Huston M.R., Howe R.T. and Maboudian R., Effect of hydrogen termination on the work of adhesion between rough polycrystalline silion surface, J. Appl Phys, Vol.81, 1997, 3474–3483.

    Article  Google Scholar 

  3. Letechtnberg R., Timans H.A.C., Elders J. and Elwenspoek M., Stiction of surface micromachined structures after rinsing and drying-model and investigation of adhesion mechanisms, Sensors and Actuators, Vol.43(A), 1994, 230–238.

    Article  Google Scholar 

  4. Lawn B., Fracture of Brittle Solid, 2nd edn, New York: Cambridge University Press, 1993.

    Book  Google Scholar 

  5. Mastrangelo C.H. and Hsu C.H., Mechanical stability and adhesion of microstructures under capillary force—Part I: basic theory, J. Micro-Electro-Mech, Sys.2, 1993, 33–43.

    Article  Google Scholar 

  6. de Boer M.P. and Michalske T.A., Accurate method for determining adhesion of cantilever beams, J. Apple, Phys.86, 1999, 817–827.

    Article  Google Scholar 

  7. Jones E.E., Begley M.R. and Murphy K.D., Adhesion of micro-cantilevers subjected to mechanical point loading: modeling and experiments, J. Mech. Phys. Solid, Vol.51, 2003, 1601–1622.

    Article  Google Scholar 

  8. Johnson K.L., Kendall K. and Robbers D., Surface energy and contact of elastic solid, Pro. R. Soc. London, Vol.324(A), 1971, 301–313.

    Article  Google Scholar 

  9. Maugis D., Adhesion of sphere: the JKP-DMT transition using a Dugdal mode, Colloid Interface Sci, Vol.192(A), 1997, 326–333.

    Google Scholar 

  10. Johnson K.L., Adhesion and friction between a smooth elastic spherical asperity and a plane surface, Pro. R. Soc. Lond., Vol.453(A), 1997, 163–179.

    Article  Google Scholar 

  11. Burnham N.A. and Colton R.J., Force microscopy //Bonnell, D.A.(ed.), Scanning Tunneling Microscopy and Sperctroscopy, New York: VCH Publishers, 1993, 191–249.

    Google Scholar 

  12. Zdeblick M.J. and Angell J.B., A microminiature electric-fluidic valve //Trimmer, W.S.(ed.), Micromechanics and MEMS, New York: IEEE Press, 1996, 444–449.

    Google Scholar 

  13. Chien,W.Z. and Yeh,K.Y., On the large deflection of rectangular plate, Proceedings of IX-th International Congress of Applied Mechanics, Bruxelles, 1956, 403–412.

  14. Yang Fuqian, Adhesion contact of axisymmetric suspended miniature structures, Sensor Actuators, Vol.104(A), 2003, 44–52.

    Article  Google Scholar 

  15. Kendall K., Ahesion and surface energy of elastic solid, J. Phys., D: Appl, Pys.324(A), 1971, 1187–1191.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by the National Natural Science Foundation of China (No. 10572049).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fu, Y., Li, S. & Tian, Y. Adhesive contact problem of axisymmetric miniature circular plates with central rigid bump. Acta Mech. Solida Sin. 19, 341–351 (2006). https://doi.org/10.1007/s10338-006-0641-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-006-0641-5

Key words

Navigation