Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics

Kamlah, Marc; Tsakmakis, Ch.

doi:10.1016/s0020-7683(98)00040-7

Cited by 221 publications

(185 citation statements)

References 22 publications

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“…The dielectric behavior is thereby described with the help of a hyperbolic function. Another phenomenological model for ferroelectric materials has been advocated by Kamlah and Tsakmakis [23] which is straightforwardly based on the introduction of reasonable internal variables. The constitutive behavior is governed by appropriate ordinary differential equations capturing the history dependence of the material.…”

Section: Introductionmentioning

confidence: 99%

Studies on rate-dependent switching effects of piezoelectric materials using a finite element model

Arockiarajan

Delibas

Menzel

et al. 2006

Computational Materials Science

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The main goal of this paper consists in the modeling of rate-dependent behavior of piezoelectric materials within a three-dimensional finite element setting. We propose a rate-dependent polarization framework which is applied to cyclic electrical loading at various frequencies. The reduction in free energy of a grain is used as a criterion for the onset of the domain switching process. Nucleation in new grains and propagation of the domain walls during domain switching is modeled by a linear kinetics theory. Averaging over all individual grains renders the macroscopic response of the bulk material. Intergranular effects, which are essential for realistic simulations, are phenomenologically captured via a probabilistic approach. The presented numerical examples, as based on the proposed three-dimensional finite element framework, are related to the simulation of PIC-151 ceramics. In particular, averaged electric displacement versus electric field curves are plotted and compared with experimental data reported in the literature.

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Section: Introductionmentioning

confidence: 99%

Studies on rate-dependent switching effects of piezoelectric materials using a finite element model

Arockiarajan

Delibas

Menzel

et al. 2006

Computational Materials Science

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“…A representative set of state variables is thereby adopted and incorporated into essential expressions and functions such as the free energy. Further constitutive relations and evolution equations are then established by taking fundamental thermodynamic considerations into account; see for instance Lynch and McMeeking (1994), Kamlah and Tsakmakis (1999), Landis (2002) or Schröder and Romanowski (2005). When setting up such phenomenologically motivated theories, one generally has the choice whether to fix material properties or to allow the material properties to change during the deformation process.…”

Section: Introductionmentioning

confidence: 99%

Computational modeling of rate-dependent domain switching in piezoelectric materials

Arockiarajan

Menzel

Delibas

et al. 2006

European Journal of Mechanics - A/Solids

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In this contribution a micromechanically motivated model for rate-dependent switching effects in piezoelectric materials is developed. The proposed framework is embedded into a three-dimensional finite element setting whereby each element is assumed to represent an individual grain. Related dipole (polarization) directions are thereby initially randomly oriented at the element level to realistically capture the originally un-poled state of grains in the bulk ceramics. The onset of domain switching processes is based on a representative energy criterion and combined with a linear kinetics theory accounting for time-dependent propagation of domain walls during switching processes. In addition, grain boundary effects are incorporated by making use of a macromechanically motivated probabilistic approach. Standard volume-averaging techniques with respect to the response on individual grains in the bulk ceramics are later on applied to obtain representative hysteresis and butterfly curves under macroscopically uniaxial loading conditions at different loading frequencies. It turns out that the simulations based on the developed finite element formulation nicely match experimental data reported in the literature.

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“…In order to simulate the characteristic polarization and mechanical butterfly hysteresis loops for ferroelectric solids, we employ a three-dimensional Preisach model. In detail, we decompose the dielectric displacement and mechanical deformations into a linear reversible and a non-linear irreversible part, see [4]. The irreversible part of the dielectric displacement, which describes the remanent polarization of the material, is approximated with a Preisach operator, see [2,3,[6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Computational characterization of ferroelectric solids with a 3D Preisach model based on an orientation distribution function

Labusch

Schröder

2016

Proc Appl Math and Mech

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Ferroelectric or ferromagnetic materials show an interaction between mechanical deformations and polarization or magnetization. A few multiferroic materials possess both ferroic properties and exhibit a magneto-electric (ME) coupling. These ME properties can be achieved in two-phase composites, which combine ferroelectric and ferromagnetic characteristics. To predict a realistic material behavior and a more precise ME coefficient, the application of suitable material models which describe the nonlinear hysteretic behavior is of particular importance. In the present contribution we focus on the characterization of a nonlinear ferroelectric material behavior, in terms of a 3D Preisach model based on an orientation distribution function.

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Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics

Cited by 221 publications

References 22 publications

Studies on rate-dependent switching effects of piezoelectric materials using a finite element model

Studies on rate-dependent switching effects of piezoelectric materials using a finite element model

Computational modeling of rate-dependent domain switching in piezoelectric materials

Computational characterization of ferroelectric solids with a 3D Preisach model based on an orientation distribution function

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