A thermodynamic consistent 1D model for ferroelastic and ferroelectric hysteresis effects in piezoceramics

Communications in Numerical Methods in Engineering

Volumn 22, Issue 7, 2006, Pages 727-739

  Klinkel, Sven ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Constitutive law; Ferroelastic; Ferroelectric; Finite element method; Hysteresis; Mechanical depolarization; Piezoceramic

Indexed keywords

CERAMIC MATERIALS; DEGREES OF FREEDOM (MECHANICS); ELECTRIC FIELDS; ELECTRIC POTENTIAL; FERROELECTRICITY; FINITE ELEMENT METHOD; FREE ENERGY; HARDENING; HYSTERESIS; PIEZOELECTRIC MATERIALS; POLARIZATION; REMANENCE;

CONSTITUTIVE LAW; FERROELASTIC; MECHANICAL DEPOLARIZATION; PIEZOCERAMIC;

THERMODYNAMICS;

CERAMIC MATERIALS; DEGREES OF FREEDOM (MECHANICS); ELECTRIC FIELDS; ELECTRIC POTENTIAL; FERROELECTRICITY; FINITE ELEMENT METHOD; FREE ENERGY; HARDENING; HYSTERESIS; PIEZOELECTRIC MATERIALS; POLARIZATION; REMANENCE; THERMODYNAMICS;

EID: 33745820351     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.845     Document Type: Article

References (24)

1. Huber JE, Fleck NA, Landis CM, McMeeking RM. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids 1999; 47:1663-1697.
2. Huber JE, Fleck NA. Multi-axial electrical switching of a ferroelectric: theory versus experiment. Journal of the Mechanics and Physics of Solids 2001; 49:785-811.
3. Bassiouny E, Ghaleb AF, Maugin GA. Thermodynamical formulation for coupled electromechanical hysteresis effects - I. Basic equations. International Journal of Engineering Science 1988; 26(12):1279-1295.
4. Bassiouny E, Ghaleb AF, Maugin GA. Thermodynamical formulation for coupled electromechanical hysteresis effects - II. Poling of ceramics. International Journal of Engineering Science 1988; 26(12):1297-1306.
5. Bassiouny E, Maugin GA. Thermodynamical formulation for coupled electromechanical hysteresis effects - III. Parameter identification. International Journal of Engineering Science 1989; 27(8):975-987.
6. Bassiouny E, Maugin GA. Thermodynamical formulation for coupled electromechanical hysteresis effects - IV. Combined electromechanical loading. International Journal of Engineering Science 1989; 27(8):989-1000.
7. Elhadrouz M, Zineb TB, Patoor E. Constitutive law for ferroelastic and ferroelectric piezoceramics. Journal of Intelligent Material Systems and Structures 2005; 16:221-263.
8. Kamlah M, Tsakmakis C. Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics. International Journal of Solids and Structures 1999; 36:669-695.
9. Kamlah M. Ferroelectric and ferroelastic piezoceramics - modeling of electromechanical hysteresis phenomena. Continuum Mechanics and Thermodynamics 2001; 13:219-268.
10. Landis CM. Fully coupled multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. Journal of Mechanics and Physics of Solids 2002; 50:127-152.
11. McMeeking RM, Landis CM. A phenomenological multi-axial constitutive switching in polycrystalline ferroelectric ceramics. International Journal of Engineering Science 2002; 40:1553-1577.
12. Schröder J, Romanowski H. A simple coordinate invariant thermodynamic consistent model for nonlinear electro-mechanical coupled ferroelectrica. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, 2004.
13. Preisach E. Über die magnetische Nachwirkung. Zeitschrift für Physik 1935; 94:277-302.
14. Butz A, Klinkel S, Wagner W. A nonlinear piezoelectric 3D-beam finite element formulation. In Proceedings Third MIT Conference on Computational Fluid and Solid Mechanics, Bathe K-J (ed.). Massachusetts Institute of Technology: Cambridge, MA, 2005; 291-296.
15. Hwang SC, Lynch CS, McMeeking RM. Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metallurgica et Materialia 1995; 43:2073-2084.
16. Simkovics R. Nichtlineares piezoelektrisches Finite-Elemente-Verfahren zur Modellierung piezokeramischer Aktoren. Ph.D. Thesis, Universität Erlangen-Nümberg, 2002.
17. Schröder J, Gross D. Invariant formulation of the electromechanical enthalpy function of transverly isotropic piezoelectric materials. Archives of Applied Mechanics 2004; 73:533-552.
18. Gaudenzi P, Bathe KJ. An iterative finite element procedure for the analysis of piezoelectric continua. Journal of Intelligent Material Systems and Structures 1995; 6(2):266-273.
19. Benjeddou A. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Computers and Structures 2000; 76:347-363.
20. Klinkel S, Wagner W. A geometrically nonlinear piezoelectric solid shell element based on a mixed multi-field variational formulation. International Journal for Numerical Methods in Engineering, in press.
21. Ghandi K, Hagood NW. A hybrid finite element model for phase transitions in nonlinear electro-mechanically coupled material. In Smart Structures and Materials: Proceedings of SPIE, vol. 3039, Varadan V, Chandra J (eds). SPIE: Bellingham, 1997; 97-112.
22. Ikeda T. Fundamentals of Piezoelectricity. ORD University Press: Oxford, 1990.
23. Wriggers P. Nichtlineare Finite-Element-Methoden. Springer: Berlin, 2001.
24. Lynch CS. The effect of uniaxial stress on the electro-mehcnical response of 8/65/35 PLZT. Acta Materialia 1996; 44:4137-4148.