A thermodynamically and microscopically motivated constitutive model for piezoceramics

Kamlah, Marc; Wang, Zhenggui

doi:10.1016/j.commatsci.2003.08.002

Cited by 30 publications

(24 citation statements)

References 14 publications

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“…A constitutive model based on microscopically motivated internal variables is proposed in [20], where depolarization effects have also been taken into account. A multiaxial thermodynamically consistent realization of the description of ferroelectric ceramics is presented in [21] (see also [9]), where the postulated switching surfaces and associated flow rules guarantee a positive dissipation during switching.…”

Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting

Schröder

Romanowski

2005

Arch Appl Mech

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In this contribution we present a phenomenological mesoscopic thermodynamically consistent model for the description of switching processes in ferroelectric materials that is able to describe the fundamental electromechanical hysteresis effects. The main goal is to develop a representation using the set of independent variables, the strains and the electric field, in a coordinate-invariant setting. This formulation is particularly suitable for the treatment of a variety of complex boundary-value problems (BVP) with regard to the essential boundary conditions. Here we restrict ourselves to transversely isotropic solids. The anisotropic behavior is governed by isotropic tensor functions that depend on a finite set of invariants. Thus the material symmetry requirements are automatically fulfilled.

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Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting

Schröder

Romanowski

2005

Arch Appl Mech

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“…Our class of models is stimulated by the engineering models from [3,4,5,7,8]. However, we will rephrase the theory there in such a way that it can be formulated in terms of two energetic functionals, namely the stored energy E and the pseudo-potential R for the dissipation.…”

Section: Modeling For Ferroelectric Materialsmentioning

confidence: 99%

“…It is based on the rate-independent, three-dimensional models used in the engineering literature, see [1,2,3,4,5,6,7,8,9]. These models work in the framework of small deformations and the quasistatic approximation for the elastic and electrostatic equilibria.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analytical Study for Ferroelectric Materials

Mielke

Timofte

2006

Mechanics of Advanced Materials and Structures

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Abstract. We discuss rate-independent engineering models for multi-dimensional behavior of ferroelectric materials. These models capture the non-linear and hysteretic behavior of such materials. We show that these models can be formulated in an energetic framework which is based on the elastic and the electric displacements as reversible variables and interior, irreversible variables like the remanent polarization. We provide quite general conditions on the constitutive laws which guarantee the existence of a solution. Under more restrictive assumptions we are also able to establish uniqueness results.

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“…The Clausius-Duhem inequality is then used as the basis for the development of the evolution of these internal variables by means of a dissipation potential. A simple macroscopic constitutive model with remanent polarization and remanent strain as internal variables was developed by Kamlah and his coworkers [32]- [35]. A series of work on constitutive modeling of ferroelectric ceramics has been published recently by McMeeking's group [36]- [41].…”

Section: Introductionmentioning

confidence: 99%

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Liu

Wang

2008

Acta Mech

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Summary. Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u i , electric displacement D i and volume fraction q I of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction q I of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction q I of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction q I of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

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A thermodynamically and microscopically motivated constitutive model for piezoceramics

Cited by 30 publications

References 14 publications

A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting

A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting

Modeling and Analytical Study for Ferroelectric Materials

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

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