Determination of the polar equilibrium properties of the ferroelectric ceramic PZT 65/35

Energy functions and basic equations for ferroelectrics

“…Several nonlinear constitutive models were proposed and these different types of constitutive models for the ferroelectric ceramics can generally fall into two categories [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. One category is based on the micro-electromechanical behavior of grains and another on the macro phenomenological model.…”

“…The macro phenomenological models [9][10][11][12][13][14][15][16][17][18][19], which are mainly based on the first and second laws of thermodynamics and the postulate of maximum dissipation, consist of a selection of the internal variables characterizing the thermodynamic state of the material, a description for a switching surface (just analogous to a yield surface in conventional plasticity theory), a flow rule, and a derivation of the evolution equations of these internal variables. They usually give a purely macroscopic picture and do not describe the microstructural changes that accompany the process of polarization and domain switching.…”

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

“…(17) is due to the term of Dd (I) kij r ij E k , hence in order to simplify the finite element calculation procedure, following Hwang et al [10], McMeeking and Landis [29], Kamlah [37] and Arockiarajan et al [57], the ferroelectric material is assumed to be isotropic elastic and isotropic dielectric, but the piezoelectricity coefficient d…”

“…Thermodynamic principles are then used to derive further expressions. Chen and his cooperators [26]- [29] proposed the phenomenological model to describe the electromechanical coupling characters of ferroelectric material. Their model was quite complex and limited to uniaxial electrical loading.…”

Nonlinear constitutive behavior of ferroelectric materials

“…In order to make the complex ferroelectric nonlinear constitutive behavior available for structural mechanical analysis, the phenomenological models with fewer internal variables have been developed. Chen and his cooperators [16][17][18][19] proposed the phenomenological model to describe the electromechanical coupling characteristics of the ferroelectric material. They used the remnant polarization and the remnant strain as the internal variables and they only considered the uniaxial loading.…”