Skip to main content
SpringerLink
Log in

Neutral-coated circular piezoelectric inclusions

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This study is concerned with the neutrality of a coated circular piezoelectric inclusion when the matrix is subjected to remote uniform electroelastic loadings. Two design schemes are proposed to make the coated inclusion neutral. In the first scheme, the thickness of the coating can be designed for given electroelastic constants of the composite so as to make the inclusion neutral to certain remote uniform loadings. In the second scheme, the electroelastic constants of the coating can be designed for given electroelastic constants of the inclusion and the matrix, and given coating thickness so as to make the inclusion neutral to any remote uniform loadings. The analysis indicates that even in the absence of the coating, the piezoelectric inclusion can be made neutral if the electroelastic constants of the two-phase composite satisfy a restriction.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Weng G.J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984)

    Article  MATH  Google Scholar 

  2. Zhao Y.H., Weng G.J.: Plasticity of a two-phase composite with partially debonded inclusions. Int. J. Plast. 12, 781–804 (1996)

    Article  MATH  Google Scholar 

  3. Liu Y.W., Fang Q.H., Jiang C.P.: A piezoelectric screw dislocation interacting with an interphase layer between a circular inclusion and the matrix. Int. J. Solids Struct. 41, 3255–3274 (2004)

    Article  MATH  Google Scholar 

  4. Liu Y.W., Fang Q.H., Jiang C.P.: Interaction between an edge dislocation and a circular inclusion with interfacial rigid lines. Acta Mech. 180, 157–174 (2005)

    Article  MATH  Google Scholar 

  5. Fang Q.H., Liu Y.W.: Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects. Acta Mater. 54, 4213–4220 (2006)

    Article  Google Scholar 

  6. Wang G.F., Feng X.Q., Yu S.W.: Interface effects on the diffraction of plane compressional waves by a nanosized spherical inclusion. J. Appl. Phys. 102, 043533-1–043533-6 (2007)

    Google Scholar 

  7. Dundurs J., Markenscoff X.: Stress fields and Eshelby forces on half-plane inhomogeneities with eigenstrains and strip inclusions meeting a free surface. Int. J. Solids Struct. 46, 2481–2485 (2009)

    Article  MATH  Google Scholar 

  8. Fang Q., Jin B., Liu Y.: Interaction between screw dislocations and inclusions with imperfect interfaces in fiber-reinforced composites. Acta Mech. 203, 113–125 (2009)

    Article  MATH  Google Scholar 

  9. Pan Y., Weng G.J., Meguid S.A., Bao W.S., Zhu Z.H., Hamouda A.M.S.: Percolation threshold and electrical conductivity of a two-phase composite containing randomly oriented ellipsoidal inclusions. J. Appl. Phys. 110, 123715 (2011)

    Article  Google Scholar 

  10. Markenscoff X., Ni L.: Driving forces and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrain. Q. Appl. Math. 69, 529–548 (2011)

    MATH  MathSciNet  Google Scholar 

  11. Luo J., Liu F.: Stress analysis of a wedge disclination dipole interacting with a circular nanoinhomogeneity. Eur. J. Mech. A Solids 30, 22–32 (2011)

    Article  MATH  Google Scholar 

  12. Li Z., Li J., Sun J., Feng X.Q.: An approximate continuum theory for interaction between dislocation and inhomogeneity of any shape and properties. Appl. Phys. 109, 113529-1–113529-7 (2011)

    Google Scholar 

  13. Zhou K., Keer L.M., Wang Q.J.: Semi-analytic solution for multiple interacting three-dimensional inhomogeneous inclusions of arbitrary shape in an infinite space. Int. J. Numer. Meth. Eng. 87, 617–638 (2011)

    Article  MATH  Google Scholar 

  14. Zhou K., Keer L.M., Wang Q.J., Ai X., Sawamiphakdi K., Glaws P., Paire M., Che F.: Interaction of multiple inhomogeneous inclusions beneath a surface. Comput. Methods. Appl. Mech. Eng. 217–220, 25–33 (2012)

    Article  Google Scholar 

  15. Wang X., Zhou K.: Long-range interaction of a line dislocation with multiple multicoated inclusions of arbitrary shape. Acta Mech. 224, 63–70 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang X., Zhou K.: Three-phase piezoelectric inclusions of arbitrary shape with internal uniform electroelastic field. Int. J. Eng. Sci. 63, 23–29 (2013)

    Article  Google Scholar 

  17. Mansfield E.H.: Neutral holes in plane stress-reinforced holes which are elastically equivalent to the uncut sheet. Q. J. Mech. Appl. Math. 6, 370–378 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  18. Milton G.W., Serkov S.K.: Neutral coated inclusions in conductivity and anti-plane elasticity. Proc. R. Soc. Lond. A457, 1973–1997 (2001)

    Article  MathSciNet  Google Scholar 

  19. Chen T., Benveniste Y., Chuang P.C.: Exact solutions in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages. Proc. R. Soc. Lond. A458, 1719–1759 (2002)

    Article  Google Scholar 

  20. Schiavone P.: Neutrality of the elliptic inhomogeneity in the case of non-uniform loading. Int. J. Eng. Sci. 41, 2081–2090 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Bertoldi K., Bigoni D., Drugan W.J.: Structural interfaces in linear elasticity. Part II: effective properties and neutrality. J. Mech. Phys. Solids 55, 35–63 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Benveniste Y., Miloh T.: Soft neutral elastic inhomogeneities with membrane-type interface. J. Elast. 88, 87–111 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  23. Jarczyk P., Mityushev V.: Neutral coated inclusions of finite conductivity. Proc. R. Soc. Lond. A468, 954–970 (2012)

    Article  Google Scholar 

  24. Wang X., Schiavone P.: Neutral coated circular inclusions in finite plane elasticity of harmonic materials. Eur. J. Mech. A Solids 33, 75–81 (2012)

    Article  MathSciNet  Google Scholar 

  25. Wang X., Schiavone P.: Neutrality in the case of N-phase elliptical inclusions with internal uniform hydrostatic stresses. Int. J. Solids Struct. 49, 800–807 (2012)

    Article  Google Scholar 

  26. Kang, H., Lee, H.: Coated inclusions of finite conductivity neutral to multiple fields in two dimensional conductivity or anti-plane elasticity. arXiv:1303.7130 (2013)

  27. Ecsedi, I., Baksa, A.: Neutral spherical inhomogeneities in a twisted circular cylindrical bar. Acta Mech. doi:10.1007/s00707-013-0915-1 (2013)

  28. Lee K.Y., Lee W.G., Pak Y.E.: Interaction between a semi-infinite crack and a screw dislocation in a piezoelectric material. ASME J. Appl. Mech. 67, 165–170 (2000)

    Article  MATH  Google Scholar 

  29. Xiao Z.M., Chen B.J.: Electro-elastic stress analysis for a Zener–Stroh crack interacting with a coated inclusion in a piezoelectric solid. Acta Mech. 171, 29–40 (2004)

    Article  MATH  Google Scholar 

  30. Ru C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 559–572 (1998)

    Article  MATH  Google Scholar 

  31. Wang X., Zhou K.: Novel near-cloaking multicoated structures for screw dislocations. Mech. Mater. 55, 73–81 (2012)

    Article  Google Scholar 

  32. Zhou K., Hoh H.J., Wang X., Keer L.M., Pang J.H.L., Song B., Wang Q.J.: A review of recent works on inclusions. Mech. Mater. 60, 144–158 (2013)

    Article  Google Scholar 

  33. Milton G.W., Briane M., Willis J.R.: On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006)

    Article  Google Scholar 

  34. Liu L.P.: Neutral shells and their applications in the design of electromagnetic shields. Proc. R. Soc. Lond. A466, 3659–3677 (2010)

    Article  Google Scholar 

  35. Ammari H., Kang H., Lee H., Lim M.: Enhancement of near cloaking using generalized polarization tensors vanishing structure. Part I: the conductivity problem. Commun. Math. Phys. 317, 253–266 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  36. Ammari H., Kang H., Lee H., Lim M.: Enhancement of near cloaking. Part II: the Helmholtz equation. Commun. Math. Phys. 317, 485–502 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  37. Wang X., Sudak L.J.: A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface. Int. J. Solids Struct. 44, 3344–3358 (2007)

    Article  MATH  Google Scholar 

Download references

Author information

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

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Kun Zhou

Authors
  1. Xu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xu Wang or Kun Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, X., Zhou, K. Neutral-coated circular piezoelectric inclusions. Acta Mech 225, 1537–1543 (2014). https://doi.org/10.1007/s00707-013-1019-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-1019-7

Keywords

Search

Navigation