A nonlinear model of piezoelectric polycrystalline ceramics under quasi-static electromechanical loading

Delibas, Bülent; Arockiarajan, A.; Seemann, Wolfgang

doi:10.1007/s10854-005-2725-2

Cited by 11 publications

(13 citation statements)

References 21 publications

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“…(2) Micromechanical models that consider the material on the level of single grains, see, for example, Delibas et al [9], Fröhlich [10], Huber and Fleck [13], Belov and Kreher [4], Huber [12], McMeeking et al [28], Smith and Hu [35].…”

Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

Kaltenbacher

Krejčı́

2015

Z. Angew. Math. Mech.

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We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well-posed under the hypothesis that hysteretic effects take place only in one preferred direction. We prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.

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Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

Kaltenbacher

Krejčı́

2015

Z. Angew. Math. Mech.

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“…Many available theoretical studies are based on micromechanical material models [Hwang et al 1995;1998;Chen et al 1997;Chen and Lynch 1998;Huber et al 1998;Hwang 2000;Smith et al 2003;Huber and Fleck 2004;Seemann et al 2004;Delibas et al 2005;Semenov et al 2006] which have led to a better understanding of the behavior of ferroelectrics. In general an application of micromechanical models to common engineering problems is difficult because the models are mostly very complex and computationally expensive.…”

Section: Micromechanical Modelingmentioning

confidence: 99%

“…In [Kamlah et al 2005], grain to grain interaction is modeled explicitly by means of the finite element method. Seemann et al [2004] and Delibas et al [2005] have derived a model on the level of the grains of a polycrystal in which they assume that after poling the domains in a grain have the same orientation. The basis of the model is an energetic approach from [Hwang et al 1998] in which the potential energy of a single domain is taken into consideration.…”

Section: Micromechanical Modelingmentioning

confidence: 99%

Finite element implementation of nonlinear constitutive models for piezoceramic materials

Laskewitz

Kamlah

2010

JOMMS

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The objective of this work was the finite element implementation of constitutive material models for piezoceramic materials. A phenomenological material model was implemented by means of a customized radial return mapping algorithm into an open source finite element program, and the problem was reduced to the solution of a single nonlinear algebraic equation. This led to a significant reduction in computation time for simulations compared to an implementation by means of an explicit higher order integration scheme for the constitutive differential equations. Furthermore, a microscopically motivated material model was implemented by means of a radial return mapping algorithm based on the backward Euler scheme.Apart from simulations of the principal behavior of the material models and their finite element implementations, simulations of applied examples are discussed which demonstrate the properties of the models and the performance of the implementations.

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“…͑1͒ Ferroelastic strain ˆi j F is associated with the dipole orientation and hence the pseudospin state as described before. 6,14,15,17 The two ferroelastic strain states are where 0 is the spontaneous strain of a tetragonal cell along the elongated edge. ͑2͒ Elastic strain ˆi j el is a component that is due to the presence of stress wherein the material deforms elastically under a small stress or plastically for a stress exceeding the elastic limit.…”

Section: ͑3͒mentioning

confidence: 99%

Simulation of electromechanical responses of ferroelectric ceramics driven by combined alternating electrical and mechanical loadings

Chung

Chow

2007

Journal of Applied Physics

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The experimental result on dielectric and mechanical properties of PbZr x Ti 1−x O 3 driven by combined alternating electrical and mechanical loadings in various phase differences has been obtained by Zhou et al. ͓J. Appl. Phys. 96, 6634 ͑2004͔͒. This paper presents the numerical simulation of this result using a two-dimensional four state Potts model. In this model, there are four different dipole orientations to reflect the coexistence of 90°and 180°domain walls. The coupling between the electrical and mechanical responses is implemented by the presence of two different ferroelastic strain states which are associated to the four different dipole orientations. The interactions of these dipoles and strains together with the mechanical energy density are incorporated into the system Hamiltonian. The enhanced and reduced electromechanical responses when the electric field and the compressive stress are out of phase and in phase, respectively, are reproduced by our model.

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A nonlinear model of piezoelectric polycrystalline ceramics under quasi-static electromechanical loading

Cited by 11 publications

References 21 publications

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

Finite element implementation of nonlinear constitutive models for piezoceramic materials

Simulation of electromechanical responses of ferroelectric ceramics driven by combined alternating electrical and mechanical loadings

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