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

This paper represents a macroscopic constitutive law for domain switching effects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the Helmholtz free energy and a switching surface. In the general sense of a kinematic hardening process, the movement of the centre of the switching surface is controlled by internal variables. In common usage, these are the remanent polarization and the irreversible strain. The novel aspect of the present work is to introduce an irreversible electric field, which serves besides the irreversible strain as internal variable. The irreversible electric field has only theoretical meaning, but it makes the formulation very suitable for a finite-element implementation, where displacement and the electric potential are the nodal degrees of freedom. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for piezoelectric ceramics. Furthermore, it accounts for the mechanical depolarization effect, which occurs if the polarized piezoceramic is subjected to a compression stress. Copyright © 2005 John Wiley & Sons, Ltd.

[1]  K. Bathe,et al.  An Iterative Finite Element Procedure for the Analysis of Piezoelectric Continua , 1995 .

[2]  Marc Kamlah,et al.  Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics , 1999 .

[3]  Norman A. Fleck,et al.  Multi-axial electrical switching of a ferroelectric: theory versus experiment , 2001 .

[4]  Gérard A. Maugin,et al.  Thermodynamical formulation for coupled electromechanical hysteresis effects—IV. Combined electromechanical loading , 1989 .

[5]  F. Preisach.  Über die magnetische Nachwirkung , 1935 .

[6]  Gérard A. Maugin,et al.  Thermodynamical formulation for coupled electromechanical hysteresis effects—II. Poling of ceramics , 1988 .

[7]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .

[8]  Gérard A. Maugin,et al.  Thermodynamical formulation for coupled electromechanical hysteresis effects. III: Parameter identification , 1989 .

[9]  Chad M. Landis,et al.  Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics , 2002 .

[10]  Tarak Ben Zineb,et al.  Constitutive Law for Ferroelastic and Ferroelectric Piezoceramics , 2005 .

[11]  Gérard A. Maugin,et al.  Thermodynamical formulation for coupled electromechanical hysteresis effects—I. Basic equations , 1988 .

[12]  Christopher S. Lynch,et al.  The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT , 1996 .

[13]  M. Kamlah,et al.  Ferroelectric and ferroelastic piezoceramics – modeling of electromechanical hysteresis phenomena , 2001 .

[14]  Norman A. Fleck,et al.  A constitutive model for ferroelectric polycrystals , 1999 .

[15]  Chad M. Landis,et al.  A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics , 2002 .

[16]  Jörg Schröder,et al.  Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials , 2004 .

[17]  Christopher S. Lynch,et al.  Ferroelectric/ferroelastic interactions and a polarization switching model , 1995 .

[18]  Jörg Schröder,et al.  A simple coordinate invariant thermodynamic consistent model for nonlinear electro-mechanical coupled ferroelectrica , 2004 .

[19]  Peter Wriggers,et al.  Nichtlineare Finite-Element-Methoden , 2001 .