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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

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Laboratory of Physics of Materials, Faculty of Sciences of Sfax, University of Sfax, PB 815, 3018, Sfax, Tunisia

    Farid Takali, Souhir Msedi, Anouar Njeh & Mohamed Hedi Ben Ghozlen

  2. National School of Engineers of Sfax (ENIS), Street Soukra Km 4, 3018, Sfax, Tunisia

    Farid Takali

  3. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    Cherif Othmani

  4. Strukturforschung, Fachbereich 11, Material-und Geowissenschaften, Technical University Darmstadt, Alarich-Weiss-Strasse 2, 64287, Darmstadt, Germany

    Wolfgang Donner

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  1. Farid Takali
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  2. Souhir Msedi
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  3. Cherif Othmani
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  4. Anouar Njeh
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  6. Mohamed Hedi Ben Ghozlen
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Correspondence to Farid Takali.

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Takali, F., Msedi, S., Othmani, C. et al. 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. Acta Mech 230, 1027–1035 (2019). https://doi.org/10.1007/s00707-018-2316-y

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  • DOI: https://doi.org/10.1007/s00707-018-2316-y

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