Modelisation de materiaux piezoelectriques et electrostrictifs par Ia methode des elements finis

Authors

  • Bertrand Dubus Institut d'Electronique et de Microelectronique du Nord, UMR 8520, departement /SEN 41, boulevard Vauban, F-59046 Lille cedex
  • Jean-Claude Debus Institut d'Electronique et de Microelectronique du Nord, UMR 8520, departement /SEN 41, boulevard Vauban, F-59046 Lille cedex
  • Jocelyne Coutte Institut d'Electronique et de Microelectronique du Nord, UMR 8520, departement /SEN 41, boulevard Vauban, F-59046 Lille cedex

Keywords:

pie::oelectricity, electrostriction, electromechanical transduction, electromechanical coupling, finite element method

Abstract

Numerical models used to describe the electromechanical coupling due to pie::oelectric or electrostrictive effects are analysed In the first section, the thermodynamic basis provides constitutive equations of pie::oelectricity and electrostriction in a similar form. The principle of virtual works leads to a unique variational formulation of both effects. This formulation is derived for static and dynamic problems in the second section. The finite element discreti::ation and the application of the variational principle provide linear or nonlinear coupled set of equations. In the third section, two applications are presented: an ultrasonic 110/or made of PZT ceramics for pie::oelectricity, a PMN-PT bar for electrostriction.

Downloads

Download data is not yet available.

References

[ALL 70] ALLIK H., HUGHES T.J.R., «Finite element method for piezoelectric vibration»,

Int. J. Num. Met h. Eng. vol. 2, 1970, p. 151-157.

[A TI 98] AT/LA finite element code for piezoelectric and magnetostrictive transducers

modeling, version 5./.I, user's manual, lnstitut Superieur d'Electronique du Nord, Lille,

[AUL 90] AULD B.A., Acoustic fields and waves in solids. 2eme edition, Krieger Publishing

Company, Malabar, 1990.

[BER 64] BERLINCOURT D.A., CURRAN D.R., JAFFE H., « Piezoelectric and piezomagnetic

materials and their function in transducers », Physical acoustics, principles and methods

vol. !A edite par W.P. Mason, Academic Press, New York, 1964, p. 169-270.

[BUC 98] BuCHAILLOT L., BONNAMY A., « Integration d'un moteur piezoelectrique dans un

equipement aeronautique », Actes du Congres MAGELEC 98, ENSEEIHT, Toulouse,

, p. 131-137.

[CAD 46] CADY W.G., Piezoelectricity, Dover, New York, 1964.

[COU 97] COUTIE J., DEBUS J.-C., DUBUS B., BOSSUT R., «Non-linear time domain analysis

of electrostrictive materials by the finite element method » J. Acoust. Soc. Am. vol. I 0 I,

, p. 3165.

[DEB 98] DEBUS J.-C., DUBUS B., COUTTE J., « Finite element modeling of lead magnesium

niobate electrostrictive materials: static analysis», J. Acoust. Soc. Am. vol. 103. 1998,

p. 3336-3343.

[DEC 84] DECARPIGNY J.-N., « Application de Ia methode des elements finis il !'etude de

transducteurs piezoelectriques », These de Doctorat d'Etat, Universite des Sciences et

Techniques de Lille, 1984.

[DHA 82] DHATT G., TOUZOT G., Introduction a Ia methode des elements finis, Collection

Universite de Compiegne, Maloine, 1982.

[HOL 67] HOLLAND R., « Representation of dielectric, elastic and piezoelectric losses by

complex coefficients», IEEE Trans. on Sanies and Ultrason. vol. 14, 1967, p. 18-20.

[HOM 94] HOM C.L., SHANKAR N., «A fully coupled constitutive model for electrostrictive

ceramic materials », J. of Intel!. Mater. Syst. and Struc. vol. 5, 1994, p. 795-80 I.

[IKE 72] IKEDA T., « On the relations between electromechanical coupling coefficients and

elastic constants in piezoelectric crystals», Jpn. J. Appl. Phys. vol. II, 1972, p. 463.

[MAC 96] Me LAUGHLIN E.A., POWERS J.M., MOFFETT M.B., JANUS R.S., « Characterization

of PMN-PT-La for use in high-power electrostrictive projectors», J. Acoust. Soc. Am.

vol. 100, 1996, p. 2729.

[MAS 50] MASON W.P., Piezoelectric crystals and their application to ultrasonics, D. Van

Nostrand Company, Princeton, 1950.

[MAS 66] MASON W.P .. Crystal physics of interaction processes. Academic Press, New

York, 1966.

(MEl 73] MEITZLER A.H., O'BRIAN H.M .. TIERSTEN H.F., « Definition and measurement of

radial mode coupling factors in piezoelectric ceramics with large variations in Poisson's

ratio». IEEE Trans. on Sanies and Ultrason. vol. 20, 1973. p. 233.

[NYE 57] NYE J.F., Physical properties of crystals, Oxford, Londres. 1957.

[SAS 85] SASHIDA T., « Motor utilizing ultrasonic oscillation» U.S. Patent 4,562,374, 1985.

p. 12-31.

[SMI 78] SMITS J.G .. « Eigenstates of coupling factor and loss factor of piezoelectric

ceramics», These de Doctorat d'Etat, Universite de Twente. 1978.

[WAS 75] W ASHIZU K., Variational methods in elasticity and plasticity, 2eme edition,

Pergamon Press, Oxford, 1975.

[WIL 88] WILSON 0.8., Introduction to theory and design of sonar transducer, Peninsula

Publishing, Los Altos, 1988.

[ZIE 87] ZIENKIEWJCZ O.C., Wood W.L., « Transient response analysis», Finite element

handbook, edite par H. Kardestuncer, McGraw-Hill, New York, 1987, p. 2.275-2.314.

(ZIE 89] ZIENKIEWICZ O.C., TAYLOR R.L., The finite element method, 4eme edition,

McGraw-Hill, New York, 1989.

Downloads

Published

1999-05-12

How to Cite

Dubus, B. ., Debus, J.-C. ., & Coutte, J. . (1999). Modelisation de materiaux piezoelectriques et electrostrictifs par Ia methode des elements finis. European Journal of Computational Mechanics, 8(5-6), 581–606. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2989

Issue

Section

Original Article