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

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

doi:10.1016/j.commatsci.2005.08.008

Cited by 29 publications

(21 citation statements)

References 35 publications

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“…The main goal of the present study is the development of a three-dimensional coupled finite element model, extending previous elaborations by the authors reported in Arockiarajan et al (2005aArockiarajan et al ( , 2005b, to electromechanically induced rate-dependent domain switching of piezoelectric materials. The onset of domain switching is thereby initiated by means of an energy-based criterion.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…In the progression of this work, a linear kinetics theory for the propagation of new phases through the material of interest is adopted; for a detail discussion the reader is referred to Delibas et al (2006) and Arockiarajan et al (2005a). In addition to the initiation of nucleation as based on Eq.…”

Section: Rate-dependencies Based On a Volume Fraction Conceptmentioning

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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“…Alternative modelling concepts, however, incorporated such interactions present in crystalline materials by means of the so-called Eshelby inclusion method in order to provide a mean field estimate of the effective response [15][16][17][18]. Intergranular effects are explicitly considered in several models in terms of related finite element formulations [19][20][21][22][23][24][25]. The local and average energy release during domain switching in ferroelectrics are rigorously derived in [26] with application to advanced polarisation switching models.…”

Section: Introductionmentioning

confidence: 99%

Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach

et al. 2011

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A micromechanically motivated model is proposed to capture nonlinear effects and switching phenomena present in ferroelectric polycrystalline materials. The changing remnant state of the ferroelectric crystal is accounted for by means of so-called back fields-such as back stressesto resist or assist further switching processes in the crystal depending on the local loading history. To model intergranular effects present in ferroelectric polycrystals, the computational model elaborated is embedded into a mixed polygonal finite element approach, whereby an individual ferroelectric grain is represented by one single irregular polygonal finite element. This computationally efficient coupled simulation framework is shown to reproduce the specific characteristics of the responses of ferroelectric polycrystals under complex electromechanical loading conditions in good agreement with experimental observations.

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“…(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…”

Section: Principle Of Stationary Total Potential Energymentioning

confidence: 99%

“…Li and Fang [55] carried out 3D finite element simulations on ferroelectric materials. Kim and Jiang [56] and Arockiarajan et al [57] also developed a 3D finite element model for rate-dependent behavior of ferroelectric ceramics. ijk after the whole domain in the material element has switched.…”

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

Cited by 29 publications

References 35 publications

Computational modeling of rate-dependent domain switching in piezoelectric materials

Computational modeling of rate-dependent domain switching in piezoelectric materials

Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

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