Acta Mechanica

, Volume 230, Issue 3, pp 1027–1035 | Cite as

Acousto-elastic theory for the coupling parameters in terms of nonlinear elastic, piezoelectric, electrostrictive, and dielectric constants in trigonal and hexagonal crystalline systems: applied in the crystal and solid-state physics

  • Farid TakaliEmail author
  • Souhir Msedi
  • Cherif Othmani
  • Anouar Njeh
  • Wolfgang Donner
  • Mohamed Hedi Ben Ghozlen
Original Paper


The aim of the acousto-elastic theory was to measure ultrasonic velocity changes which characterize the mechanical nonlinearity of a prestressed material. In this context, our purpose is to tabulate the invariant third-order elastic coefficients including the piezoelectric, electrostrictive, and dielectric corrections. The investigation is limited to trigonal and hexagonal crystalline structures, which represent the most often encountered symmetry classes for the piezoelectric materials. In fact, the enumeration includes the high-order tensors involved in the analysis of nonlinear behaviors associated with various electromechanical coupling forms. The obtained results are extensions to previous calculations in this area which bring some corrections to certain published combinations related to the invariance rules. The numerical procedure built using the software MATLAB is based on coordinate system transformations performed on the eigenbasis of their corresponding symmetry axes three- and sixfold. In this purpose, we found some contradictions between our results and a former paper published in Journal of Applied Physics. To the authors’ knowledge, rechecking of the relationships between the invariant third-order constants and comparison with this last reference has not been discussed yet. The relationships between the invariant third-order coefficients presented in this work provide a number of attractive properties for use in mechanical and physical applications.


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The authors are grateful for the funding provided to LPM laboratory by the Tunisian Ministry of Higher Education, Scientific Research. The authors would like to thank the anonymous reviewers for their valuable comments.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Farid Takali
    • 1
    • 2
    Email author
  • Souhir Msedi
    • 1
  • Cherif Othmani
    • 3
  • Anouar Njeh
    • 1
  • Wolfgang Donner
    • 4
  • Mohamed Hedi Ben Ghozlen
    • 1
  1. 1.Laboratory of Physics of Materials, Faculty of Sciences of SfaxUniversity of SfaxSfaxTunisia
  2. 2.National School of Engineers of Sfax (ENIS)SfaxTunisia
  3. 3.Department of Civil EngineeringZhejiang UniversityHangzhouChina
  4. 4.Strukturforschung, Fachbereich 11, Material-und GeowissenschaftenTechnical University DarmstadtDarmstadtGermany

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