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Frictionless contact of a rigid punch indenting an elastic layer having piezoelectric properties

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Abstract

This article is concerned with the study of frictionless contact between a rigid punch and an elastic layer having piezoelectric properties. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the elastic layer through an applied load on it. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The relationship between the applied load and the contact area is obtained by solving the mathematically formulated problem through the use of Hankel transform of different orders. Variations of stresses and electric displacements on the surface of the layer and the piezoelectric effects on the load contact area relationship as well as normal stress have been numerically evaluated and shown graphically.

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References

  1. Galin, L.A.: Contact Problems. Springer, Berlin (2008)

    MATH  Google Scholar 

  2. Shvets, R.M., Martynyak, R.M., Kryshtofovych, A.A.: Discontinuous contact of an anisotropic half-plane and a rigid base with disturbed surface. Int. J. Eng. Sci. 34, 183–200 (1996)

    Article  MATH  Google Scholar 

  3. Chaudhuri, P.K., Ray, S.: Receding axisymmetric contact between a transversely isotropic layer and a transversely isotropic half-space. Bull. Calcutta Math. Soc. 95, 151–164 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Chaudhuri, P.K., Ray, S.: Receding contact between an orthotropic layer and an orthotropic half-space. Arch. Mech. 50, 743–755 (1998)

    MATH  Google Scholar 

  5. Comez, I., Birinci, A., Erdol, R.: Double receding contact problem for a rigid stamp and two elastic layers. Eur. J. Mech. A Solids 23, 909–924 (2004)

    Article  MATH  Google Scholar 

  6. Barik, S.P., Kanoria, M., Chaudhuri, P.K.: Contact problem for an anisotropic elastic layer lying on an anisotropic elastic foundation under gravity. J. Ind. Acad. Math. 28, 205–223 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Patra, R., Barik, S.P., Chadhuri, P.K.: Frictionless contact of a rigid punch indenting a transversely isotropic elastic layer. Int. J. Adv. Appl. Math. Mech. 3, 100–111 (2016)

    MathSciNet  Google Scholar 

  8. El-Borgi, S., Abdelmoula, R., Keer, L.: A receding contact plane problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 43, 658–674 (2006)

    Article  MATH  Google Scholar 

  9. Fabrikant, V.I.: Elementary solution of contact problems for a transversely isotropic layer bonded to a rigid foundation. Z. Angew. Math. Phys. 57, 464–490 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  11. Gladwell, M.L.: Contact Problems in the Classical Theory of Elasticity. Sijthoff and Noordhoff, Alphena (1980)

    Book  MATH  Google Scholar 

  12. Hills, D.A., Nowell, D., Sackfield, A.: Mechanics of Elastic Contacts. Butterworth-Heinemann, London (1993)

    MATH  Google Scholar 

  13. Raous, M., Jean, M., Moreau, J.J.: Contact Mechanics. Plenum Press, New York (1995)

    Book  Google Scholar 

  14. Rogowski, B.: Contact Problems for Elastic Anisotropic Media—A Series of Monographs. Technical University of Lodz, Lodz (2006)

    Google Scholar 

  15. Giannakopoulos, A.E., Suresh, S.: Theory of indentation of piezoelectric materials. Acta Mater. 47, 2153–2164 (1999)

    Article  Google Scholar 

  16. Giannakopoulos, A.E., Parmaklis, A.Z.: The contact problem of a circular rigid punch on piezomagnetic materials. Int. J. Solids Struct. 44, 4593–4612 (2007)

    Article  MATH  Google Scholar 

  17. Chen, W., Pan, E., Wang, H., Zhang, C.: Theory of indentation on multiferroic composite materials. J. Mech. Phys. Solids. 58, 1524–1551 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fan, H., Sze, K.Y., Yang, W.: Two-dimensional contact on a piezoelectric half-space. Int. J. Solids Struct. 33, 1305–1315 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rogowski, B., Kalinski, W.: The adhesive contact problem for a piezoelectric half-space. Int. J. Press. Vessels Pip. 84, 502–511 (2007)

    Article  Google Scholar 

  20. Sofonea, M., Essoufi, El-H: A piezoelectric contact problem with slip dependent coefficient of friction. Math. Model. Anal. 9, 229–242 (2004)

    MathSciNet  MATH  Google Scholar 

  21. Karapetian, E., Kachanov, M., Kalinin, S.V.: Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: applications to probing nanoelectromechanical properties of materials. J. Mech. Phys. Solids. 57, 673–688 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kirilyuk, V.S., Levehuk, O.I.: Indentation of punches into a piezoceramic body: two-dimensional contact problem of electroelasticity. Int. Appl. Mech. 44, 1244–1258 (2008)

    Article  MathSciNet  Google Scholar 

  23. Li, X.Y., Wang, M.Z.: On the anisotropic piezoelastic contact problem for an elliptical punch. Acta Mech. 186, 87–98 (2006)

    Article  MATH  Google Scholar 

  24. Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials. Int. J. Solids Struct. 37, 3201–3229 (2000)

    Article  MATH  Google Scholar 

  25. Chen, W.Q.: Inclined circular flat punch on a transversely isotropic piezoelectric half-space. Arch. Appl. Mech. 69, 455–464 (1999)

    Article  MATH  Google Scholar 

  26. Chen, W.Q.: On piezoelastic contact problem for a smooth punch. Int. J. Solids Struct. 37, 2331–2340 (2000)

    Article  MATH  Google Scholar 

  27. Ramirez, G., Heyliger, P.: Frictionless contact in a layered piezoelectric half-space. Smart Mater. Struct. 12, 612–625 (2003)

    Article  Google Scholar 

  28. Zhou, Y.T., Lee, K.Y.: Theory of moving contact of anisotropic piezoelectric materials via real fundamental solutions approach. Eur. J. Mech. A Solids 35, 22–36 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ke, L.L., Yang, J., Kitipornchai, S., Wang, Y.S.: Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch. Int. J. Solids Struct. 45, 3313–3333 (2008)

    Article  MATH  Google Scholar 

  30. Hao, T.H.: Exact solution of a flat smooth punch on a piezoelectric half plane. Mech. Res. Commun. 30, 455–461 (2003)

    Article  MATH  Google Scholar 

  31. Makagon, A., Kachanov, M., Karapetian, E., Kalinin, S.V.: Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy. Int. J. Eng. Sci. 47, 221–239 (2009)

    Article  Google Scholar 

  32. Zhou, Y.T., Lee, K.Y.: Investigation of frictional sliding contact problems of triangular and cylindrical punches on monoclinic piezoelectric materials. Mech. Mater. 69, 230–250 (2014)

    Article  Google Scholar 

  33. Ma, J., Ke, L.L., Wang, Y.S.: Electro-mechanical sliding frictional contact of a piezoelectric half-plane under a rigid conducting punch. Appl. Math. Model. 38, 5471–5489 (2014)

    Article  MathSciNet  Google Scholar 

  34. Su, J., Ke, L.L., Wang, Y.S.: Axisymmetric frictionless contact of a functionally graded piezoelectric layered half-space under a conducting punch. Int. J. Solids Struct. 90, 45–59 (2016)

    Article  Google Scholar 

  35. Su, J., Ke, L.L., Wang, Y.S.: Fretting contact of a functionally graded piezoelectric layered half-plane under a conducting punch. Smart Mater. Struct. 25, 1–21 (2016)

    Google Scholar 

  36. Su, J., Ke, L.L., Wang, Y.S.: Two-dimensional fretting contact analysis of piezoelectric materials. Int. J. Solids Struct. 73–74, 41–54 (2015)

    Article  Google Scholar 

  37. Dyka, E., Rogowski, B.: On the contact problem for a smooth punch in piezoelectroelasticity. J. Theor. Appl. Mech. 43, 745–761 (2005). Warsaw

    Google Scholar 

  38. Wang, M.Z., Xu, X.S.: A generalization of Alamnsi’s theorem and its application. Appl. Math. Model. 14, 275–279 (1990)

    Article  Google Scholar 

  39. Parton, V.Z., Kudryatvsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988)

    Google Scholar 

  40. Nowacki, W.: Teoria Sprȩżystości. PWN, Warszawa (1973)

    MATH  Google Scholar 

  41. Park, S.B., Sun, C.T.: Fracture criteria for piezoelectric ceramics. J. Am. Ceram. Soc. 78, 1475–1480 (1995)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hooghly Engineering & Technology College, Vivekananda Road, Hooghly, 712103, India

    Rajesh Patra

  2. Department of Mathematics, Gobardanga Hindu College, 24-Parganas (N), 743273, India

    S. P. Barik

  3. Department of Applied Mathematics, University of Calcutta, 92, A. P. C. Road, Kolkata, 700009, India

    P. K. Chaudhuri

Authors
  1. Rajesh Patra
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  2. S. P. Barik
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  3. P. K. Chaudhuri
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Correspondence to S. P. Barik.

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Patra, R., Barik, S.P. & Chaudhuri, P.K. Frictionless contact of a rigid punch indenting an elastic layer having piezoelectric properties. Acta Mech 228, 367–384 (2017). https://doi.org/10.1007/s00707-016-1700-8

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  • DOI: https://doi.org/10.1007/s00707-016-1700-8

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