• Julien YvonnetEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 258)


In this section, we present a procedure based on FEM for solving homogenization problems involving two coupled phenomena: electric conductivity and elasticity. In contrast to the case of thermoelasticity where the thermal problem has only an effect on the elastic problem and not the opposite, here both problems depend on the solution of each other. After presenting the localization problem defined over the RVE, the different effective operators are defined and the FEM procedure for their numerical calculation is provided. Finally, a numerical validation example is provided for fibrous piezoelectric composites.


  1. 1.
    Tichỳ J, Erhart J, Kittinger E, Prívratská J (2010) Fundamentals of piezoelectric sensorics: mechanical, dielectric, and thermodynamical properties of piezoelectric materials. Springer Science & Business Media, New YorkGoogle Scholar
  2. 2.
    Yang J (2010) Special topics in the theory of piezoelectricity. Springer Science & Business Media, New YorkGoogle Scholar
  3. 3.
    Brenner R (2009) Numerical computation of the response of piezoelectric composites using Fourier transform. Phys Rev B 79(18):184106CrossRefGoogle Scholar
  4. 4.
    Pettermann EZ, Suresh S (2000) A comprehensive unit cell model: a study of coupled effects in piezoelectric 1–3 composites. Int J Solids Struct 37(39):5447–5464CrossRefGoogle Scholar
  5. 5.
    Berger H, Kari S, Gabbert U, Rodriguez-Ramos R, Bravo-Castillero J, Guinovart-Diaz R, Sabina FJ, Maugin GA (2006) Unit cell models of piezoelectric fiber composites for numerical and analytical calculation of effective properties. Smart Mater Struct 15(2):451CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MSME LaboratoryUniversité Paris-Est Marne-la-ValléeMarne-la-Vallée Cedex2France

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