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A general treatment of piezoelectric double-inhomogeneities and their associated interaction problems

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Abstract

The present paper addresses an analytical method to determine the electroelastic fields over a double-phase piezoelectric reinforcement interacting with an ellipsoidal single-inhomogeneity. The approach is based on the extension of the electro-mechanical equivalent inclusion method (EMEIM) to the piezoelectric double-inhomogeneity system. Accordingly, the double-inhomogeneity is replaced by an electroelastic double-inclusion problem with proper polynomial eigenstrains-electric fields. The long- and short-range interaction effects are intrinsically incorporated by the homogenizing eigenfields. The equivalent double-inclusion is subsequently decomposed to the single-inclusion problems by means of a superposition scheme. The methodology is further extended to the piezoelectric multi-inhomogeneity, where the particle core is surrounded by many layers of coatings of ellipsoidal shapes. Through consideration of various examples, including (1) 2D and 3D interaction problems of a coated piezoelectric reinforcement near a lamellar inhomogeneity and (2) a two-phase spherical particle with thick coating of variable thickness, the validity and robustness of the present theory are thoroughly demonstrated.

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References

  1. He L.H., Lim C.W.: Electromechanical responses of piezoelectric fiber composites with sliding interface under anti-plane deformations. Composites Part B Eng. 34, 373–383 (2003)

    Article  Google Scholar 

  2. Fang D.N., Jiang B., Hwang K.C.: A modal for predicting effective properties of piezocomposites with non-piezoelectric inclusions. J. Elast. 62, 95–118 (2001)

    Article  MATH  Google Scholar 

  3. Dinzart F., Sabar H.: Electroelastic behavior of piezoelectric composites with coated reinforcements: Micromechanical approach and applications. Int. J. Solids Struct. 46, 3556–3564 (2009)

    Article  MATH  Google Scholar 

  4. Shiah Y.C., Huang C.H., Huang J.H.: Electromechanical responses of optical fibers with piezoelectric coatings. J. Chin. Inst. Eng. 29, 893–902 (2006)

    Article  Google Scholar 

  5. Beckert W., Kreher W., Brau W., Ante M.: Effective properties of composites fibers with a piezoelectric coating. J. Eur. Ceram. Soc. 21, 1455–1458 (2001)

    Article  Google Scholar 

  6. Jiang C.P., Cheung Y.K.: An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites. Int. J. Solids Struct. 38, 4777–4796 (2001)

    Article  MATH  Google Scholar 

  7. Sudak L.J.: Effect of an interphase layer on the electroelastic stresses within a three-phase elliptic inclusion. Int. J. Eng. Sci. 41, 1019–1039 (2003)

    Article  Google Scholar 

  8. Xiao Z.M., Bai J.: Numerical simulation on a coated piezoelectric sensor interacting with a crack. Finite Elements Anal. Design. 38, 691–706 (2002)

    Article  MATH  Google Scholar 

  9. Shen M.H., Chen S.N., Chen F.M.: Piezoelectric study on confocally multicoated elliptical inclusion. Int. J. Eng. Sci. 43, 1299–1312 (2005)

    Article  Google Scholar 

  10. Shen M.H., Chen S.N., Chen F.M.: A piezoelectric screw dislocation interacting with a nonuniformly coated circular inclusion. Int. J. Eng. Sci. 44, 1–13 (2006)

    Article  MathSciNet  Google Scholar 

  11. Shodja H.M., Ojaghnezhad F.A.: General unified treatment of lamellar inhomogeneities. Eng. Frac. Mech. 74, 1499–1510 (2007)

    Article  Google Scholar 

  12. Shodja, H.M., Kargarnovin, M.H., Hashemi, R.: Electroelastic fields in interacting piezoelectric inhomogeneities by the electro-mechanical equivalent inclusion method. Smart Materials and Structures (2010). doi:10.1088/0964-1726/19/3/035025

  13. Eshelby J.D.: The elastic field outside an ellipsoidal inclusion. Proc. R. Soc. London A. 252, 561–569 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  14. Eshelby, J.D.: Elastic inclusions and inhomogeneities progress in Solid Mechanics 2. In: Sneddon, Hill, R. (eds.). North Holland, Amsterdam, pp 89–140 (1961)

  15. Hori M., Nemat-Nasser S.: Double-inclusion model and overall moduli of multi-phase composites. Mech. Mat. 14, 189–206 (1993)

    Article  Google Scholar 

  16. Shodja H.M., Sarvestani A.S.: Elastic fields in double inhomogeneity by the equivalent nclusion method. J. Appl. Mech. 68, 3–10 (2001)

    Article  MATH  Google Scholar 

  17. Shodja H.M., Rad I.Z., Soheilifard R.: Interacting cracks and ellipsoidal inhomogeneities by the equivalent inclusion method. J. Mech. Phys. Solids 51, 945–960 (2003)

    Article  MATH  Google Scholar 

  18. Shokrolahi-Zadeh B., Shodja H.M.: Spectral equivalent inclusion method: anisotropic cylindrical multiinhomogeneities. J. Mech. Phys. Solids 56, 3565–3573 (2008)

    Article  MATH  Google Scholar 

  19. Fan H., Qin S.: A piezoelectric sensor embedded in a non-piezoelectric matrix. Int. J. Eng. Sci. 33, 379–388 (1995)

    Article  MATH  Google Scholar 

  20. Deeg, W.F.: The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. Ph.D Dissertation; Stanford University (1980)

  21. Dunn M.L., Taya M.: Micromechanics predictions of the effective electroelastic moduli of piezoelectric composite. Int. J. Solids Struct. 30, 161–175 (1993)

    Article  MATH  Google Scholar 

  22. Hashemi R., Weng G.J., Kargarnovin M.H., Shodja H.M.: Piezoelectric composites with periodic multi-coated inhomogeneities. Int. J. Solids Struct. 47, 2893–2904 (2010)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    M. H. Kargarnovin & R. Hashemi

  2. Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

    H. M. Shodja

  3. Institute for Nanoscience and Nanotechnology, Sharif University of Technology, Tehran, Iran

    H. M. Shodja

Authors
  1. M. H. Kargarnovin
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  2. H. M. Shodja
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  3. R. Hashemi
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Correspondence to M. H. Kargarnovin.

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Kargarnovin, M.H., Shodja, H.M. & Hashemi, R. A general treatment of piezoelectric double-inhomogeneities and their associated interaction problems. Acta Mech 220, 167–182 (2011). https://doi.org/10.1007/s00707-011-0464-4

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  • DOI: https://doi.org/10.1007/s00707-011-0464-4

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