Acta Mechanica

, Volume 230, Issue 10, pp 3613–3632 | Cite as

Maxwell homogenization scheme for piezoelectric composites with arbitrarily-oriented spheroidal inhomogeneities

  • R. Rodríguez-RamosEmail author
  • C. A. Gandarilla-Pérez
  • L. Lau-Alfonso
  • F. Lebon
  • F. J. Sabina
  • I. Sevostianov
Original Paper


In this work, the effective electro-elastic properties of piezoelectric composites are computed using the Maxwell homogenization method (MHM). The composites are made by several families of spheroidal inhomogeneities embedded in a homogeneous infinite medium (matrix). Each family of spheroidal inhomogeneities is made of the same material, and all the inhomogeneities have identical size and shape and are randomly oriented. The inhomogeneities and matrix materials exhibit piezoelectric transversely isotropic symmetry. It is shown that the shape of the “effective inclusion” substantially affects the effective piezoelectric properties. A new and simple form to calculate the aspect ratio of effective inclusion is presented. The effect on the overall piezoelectric properties due to the orientation of the inhomogeneities and different families of piezoelectric inhomogeneities is discussed. The MHM approach is applied in two examples, material with inhomogeneities having scatter orientation and composites with two different families of spheroidal inhomogeneities.



The funding of Proyecto Nacional de Ciencias Básicas 2013-2015 (Project No. 7515) is gratefully acknowledged. Thanks to the Mathematics and Mechanics Department at IIMAS-UNAM and FENOMEC for their support and to Ramiro Chávez Tovar and Ana Pérez Arteaga for computational assistance. The authors would like to thank the project PHC Carlos J. Finlay 2018 Project No. 39142TA (France–Cuba) and the French embassy in Havana for their support on travel expenses of PhD students in 2018. The author Rodríguez-Ramos would like to thank MyM-IIMAS-UNAM and PREI-DGAPA-UNAM for the financial support provided.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de Matemática y ComputaciónUniversidad de La HabanaHavanaCuba
  2. 2.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMexicoMexico
  3. 3.Facultad de FísicaUniversidad de La HabanaHavanaCuba
  4. 4.Instituto de Cibernética Matemática y FísicaHavanaCuba
  5. 5.CNRS, Centrale Marseille, LMAAix-Marseille UniversityMarseille Cedex 13France
  6. 6.Department of Mechanical and Aerospace EngineeringNew Mexico State UniversityLas CrucesUSA

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