Archive of Applied Mechanics

, Volume 80, Issue 4, pp 377–388 | Cite as

Influence of imperfect elastic contact condition on the antiplane effective properties of piezoelectric fibrous composites

  • Reinaldo Rodríguez-Ramos
  • Raúl Guinovart-Díaz
  • Juan C. López-Realpozo
  • Julián Bravo-Castillero
  • Federico J. Sabina


A fiber-reinforced periodic piezoelectric composite, where the constituents exhibit transverse isotropic properties, is considered. The fiber cross-section is circular and the periodicity is the same in two orthogonal directions. Imperfect mechanic contact conditions at the interphase between the matrix and fibers are represented in parametric form. In order to analyze the influence of the imperfect interface effect over the behavior of the composite, the effective axial piezoelectric moduli are obtained by means of the Asymptotic Homogenization Method. Some numerical examples are given.


Asymptotic homogenization Piezoelectric composites Linear spring interface model Imperfect contact 


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  1. 1.
    Andrianov I.V., Bolshakov V.I., Danishevs’kyy V.V., Weichert D.: Asymptotic simulation of imperfect bonding in periodic fibre-reinforced composite materials under axial shear. Int. J. Mech. Sci. 49, 1344–1354 (2007)Google Scholar
  2. 2.
    Benveniste Y.: The effective mechanical behavior of a composite with imperfect contact between the constituents. Mech. Mater. 4, 197–208 (1985)CrossRefGoogle Scholar
  3. 3.
    Benveniste Y., Miloh T.: The effective conductivity of composites with imperfect thermal contact at constituent interfaces. Int. J. Eng. Sci. 24(9), 1537–1552 (1986)MATHCrossRefGoogle Scholar
  4. 4.
    Benveniste Y.: Correspondance relations among equivalent clases of heterogenous piezoelectric solids under anti-plane mechanical and in-plane electric fields. J. Mech. Phys. Solids 43, 553–571 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Benveniste Y., Miloh T.: Imperfect soft and stiff interfaces in two dimensional elasticity. Mech. Mater. 33, 309–323 (2001)CrossRefGoogle Scholar
  6. 6.
    Bövik P.: On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17–42 (1994)MATHCrossRefGoogle Scholar
  7. 7.
    Bravo Castillero J., Guinovart Díaz R., Sabina F.J., Rodríguez Ramos R.: Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents-II. Piezoelectric and square symmetry. Mech. Mater. 33(4), 237–248 (2001)CrossRefGoogle Scholar
  8. 8.
    Bruno O.P.: The effective conductivity of strongly heterogeneous composites. Proc. R. Soc. Lond. A 433, 353–381 (1991)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Dingreville R., Qu J., Cherkaoui M.: Surface free energy and its effect on the elastic behavior of nanosized particles, wires and films. J. Mech. Phys. Solids 53, 1829–1854 (2005)MathSciNetGoogle Scholar
  10. 10.
    Duan H.L., Wang J., Huang Z.P., Karihaloo B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574–1596 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Duan H.L., Karihaloo B.L.: Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized Levin’s formula and Hill’s connections. J. Mech. Phys. Solids 55, 1036–1052 (2007)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Goland M., Reissner E.: The stresses in cemented joints. J. Appl. Mech. 11, 17–27 (1944)Google Scholar
  13. 13.
    Guinovart-Díaz R., Bravo-Castillero J., Rodríguez-Ramos R., Sabina F.J.: Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents—I. Elastic and hexagonal symmetry. J. Mech. Phys. Solids 49, 1445–1462 (2001)MATHCrossRefGoogle Scholar
  14. 14.
    Guinovart Díaz R., Rodríguez Ramos R., Bravo Castillero J., Sabina F.J., Maugin G.A.: A recursive asymptotic homogenization scheme for multi-phase fibrous elastic composites. Mech. Mater. 37, 1119–1131 (2005)CrossRefGoogle Scholar
  15. 15.
    Guinovart-Díaz R., Rodriguez-Ramos R., Bravo-Castillero J., Sabina F.J., Maugin G.A.: Closed-form thermo-elastic moduli of a periodic three-phase fiber-reinforced composite. J. Therm. Stresses 28, 1067–1093 (2005)CrossRefGoogle Scholar
  16. 16.
    Hashin Z.: Thermoelastic properties of fiber composites with imperfect interface. Mech. Mater. 8, 333–348 (1990)CrossRefGoogle Scholar
  17. 17.
    Hashin Z.: Thermoelastic properties of particulate composites with imperfect interface. J. Mech. Phys. Solids 39(6), 745–762 (1991)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Hashin Z.: The spherical inclusion with imperfect interface. J. Appl. Mech. 58, 444–448 (1991)CrossRefGoogle Scholar
  19. 19.
    Hashin Z.: Thin interphase/imperfect interface in conduction. J. Appl. Phys. 89, 2261–2267 (2001)CrossRefGoogle Scholar
  20. 20.
    Hashin Z.: Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J. Mech. Phys. Solids 50, 2509–2537 (2002)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Ikeda T.: Fundamentals of Piezoelectricity. University Press, Oxford (1990)Google Scholar
  22. 22.
    Jasiuk I., Tong T.: The effect of interface on the elastic stiffness of composites. Mech. Comput. Mat. Struct. 100, 49–54 (1989)Google Scholar
  23. 23.
    Jasiuk I., Kouider M.W.: The effect of an inhomogeneous interphase on the elastic constants of transversely isotropic composites. Mech. Mater. 15, 53–63 (1993)CrossRefGoogle Scholar
  24. 24.
    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)MATHCrossRefGoogle Scholar
  25. 25.
    Kar-Gupta, R., Venkatesh, T.A.: Electromechanical response of 1–3 piezoelectric composites: Effect of poling characteristics. J. Appl. Phys. 98, 054102-1/054102-14 (2005)Google Scholar
  26. 26.
    Lipton R., Vernescu B.: Composites with imperfect interface. Proc. R. Soc. Lond. A 452, 329–358 (1996)MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Lipton R.: Variational methods, bounds, and size effects for composites with highly conducting interface. J. Mech. Phys. Solids 45, 361–384 (1997)MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    López-López E., Sabina F.J., Bravo-Castillero J., Guinovart-Díaz R., Rodríguez-Ramos R.: Overall electromechanical properties of a binary composite with 622 symmetry constituents. Antiplane shear piezoelectric state. Int. J. Solids Struct. 42, 5765–5777 (2005)MATHCrossRefGoogle Scholar
  29. 29.
    Mahiou H., Beakou A.: Modelling of interfacial effects on the mechanical properties of fibre-reinforced composites. Compos. Part A 29A, 1035–1048 (1998)CrossRefGoogle Scholar
  30. 30.
    McPhedran R.C., McKenzie D.R.: Electrostatic and optical resonances of arrays of cylinders. Appl. Phys. 23, 223–235 (1980)CrossRefGoogle Scholar
  31. 31.
    Miller R.E., Shenoy V.B.: Size-dependent elastic properties of nano-sized structural elements. Nanotechnology 11, 139–147 (2000)CrossRefGoogle Scholar
  32. 32.
    Miloh T., Benveniste Y.: On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces. Proc. R. Soc. Lond. A 455, 2687–2706 (1999)MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Molkov, V.A., Pobedria, B.E.: Effective elastic properties of a composite with elastic contact. Izvestia Akademia Nauk SSR. Mekhanika Tverdovo Tela. No. 1. 111–117 (1988)Google Scholar
  34. 34.
    Nemat-Nasser S., Hori M.: Micromechanics: Overall Properties of Heterogeneous Materials, 2nd revised edn. Elsevier, Amsterdam (1999)Google Scholar
  35. 35.
    Nie S., Basaran C.: A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds. Int. J. Solids Struct. 42, 4179–4191 (2005)MATHCrossRefGoogle Scholar
  36. 36.
    Niklasson A.J., Datta S., Dunn M.L.: On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers. J. Acoust. Soc. Am. 91, 1875–1887 (2000)Google Scholar
  37. 37.
    Niklasson A.J., Datta S., Dunn M.L.: On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions. J. Acoust. Soc. Am. 108, 924–933 (2000)CrossRefGoogle Scholar
  38. 38.
    Parton V.Z., Kudryavtsev B.A.: Engineering Mechanics of Composite Structures. CRC Press, Boca Raton (1993)Google Scholar
  39. 39.
    Pobedria, B.E.: Mechanics of Composite Materials. Moscow University Press, Moscow (in Russian) (1984)Google Scholar
  40. 40.
    Sabina F.J, Rodríguez Ramos R., Bravo Castillero J., Guinovart Díaz R.: Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents-II: Piezoelectric and hexagonal symmetry. J. Mech. Phys. Solids 49, 1463–1479 (2001)MATHCrossRefGoogle Scholar
  41. 41.
    Sharma P., Ganti S., Bhate N.: Effect of surfaces on the size-dependent elastic state of nanoinhomogeneities. Appl. Phys. Lett. 82, 535–537 (2003)CrossRefGoogle Scholar
  42. 42.
    Shodja H.M., Tabatabaei S.M., Kamali M.T.: A piezoelectric-inhomogeneity system with imperfect interface. Int. J. Eng. Sci. 44, 291–311 (2006)CrossRefGoogle Scholar
  43. 43.
    Torquato S., Rintoul M.D.: Effect of the interface on the properties of composite media. Phys. Rev. Let. 75, 4067–4070 (1995)CrossRefGoogle Scholar
  44. 44.
    Wang J., Duan H.L., Zhang Z., Huang Z.P.: An anti-interpenetration model and connections between intherphase and interface models in particle-reinforced composites. Int. J. Mech. Sci. 47, 701–718 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Reinaldo Rodríguez-Ramos
    • 1
    • 2
  • Raúl Guinovart-Díaz
    • 1
    • 2
  • Juan C. López-Realpozo
    • 1
    • 2
  • Julián Bravo-Castillero
    • 1
    • 2
  • Federico J. Sabina
    • 3
  1. 1.Facultad de Matemática y ComputaciónUniversidad de La HabanaHabana 4Cuba
  2. 2.Campus Estado de México, División de Arquitectura e IngenieríaInstituto Tecnológico de Estudios Superiores de MonterreyMexicoMexico
  3. 3.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMexicoMexico

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