A Macroscopic Phenomenological Formulation for Coupled Electromechanical Effects in Piezoelectricity

Zhang, X.D.; Rogers, Craig A.

doi:10.1177/1045389x9300400303

Cited by 50 publications

(21 citation statements)

References 20 publications

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“…The saturation behavior of the Ising relation has also motivated its use in phenomenological models. Translates of the form P = P s tanh(E ± E c ) were employed by Zhang and Rogers [39], and r(x) = tanh(x) provides a suitable choice for the ridge functions employed in generalized Preisach, or Krasnolselskii-Pokrovskii, characterizations [2,3]. The model presented here differs in that it focuses on an energy formulation for domain processes.…”

Section: Asymptotic Polarization Relation In Absence Of Thermal Activmentioning

confidence: 99%

A Free Energy Model for Hysteresis in Ferroelectric Materials

Smith¹,

Seelecke

Ounaies

et al. 2003

Journal of Intelligent Material Systems and Structures

125

234

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This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques. In the first step of the model development, Helmholtz and Gibbs free energy relations are constructed at the lattice or domain level to quantify the relation between the field and polarization in homogeneous, single crystal compounds which exhibit uniform effective fields. The effects of material nonhomogeneities, polycrystallinity, and variable effective fields are subsequently incorporated through the assumption that certain physical parameters, including the local coercive and effective fields, are randomly distributed and hence manifestations of stochastic density functions associated with the material. Stochastic homogenization in this manner provides low-order macroscopic models with effective parameters that can be correlated with physical properties of the data. This facilitates the identification of parameters for model construction, model updating to accommodate changing operating conditions, and control design utilizing model-based inverse compensators. Attributes of the model, including the guaranteed closure of biased minor loops in quasistatic drive regimes, are illustrated through examples.i Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Section: Asymptotic Polarization Relation In Absence Of Thermal Activmentioning

confidence: 99%

A Free Energy Model for Hysteresis in Ferroelectric Materials

Smith¹,

Seelecke

Ounaies

et al. 2003

Journal of Intelligent Material Systems and Structures

125

234

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“…We note that (17) is exactly the Ising relation employed in [108] when quantifying the anhysteretic polarization and is equivalent through first-order terms with the Langevin relations employed in various ferroelectric and ferromagnetic models. Translates of the form P = P s tanh(E ± E c ) were also employed by Zhang and Rogers [123], and ridge functions of the form r(x) = tanh(x) are appropriate for generalized Preisach, or Krasnosel'skiǐ-Pokrovskiǐ characterizations [8,9,60]. The relation resulting from (5) is slightly more complicated due to the piecewise nature of the definition.…”

Section: Asymptotic Polarization Relations In the Absence Of Thermal mentioning

confidence: 99%

A unified framework for modeling hysteresis in ferroic materials

Smith

Seelecke

Dapino

et al. 2006

Journal of the Mechanics and Physics of Solids

112

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This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior. Keywords: Ferroic materials, unified models, hysteresis, constitutive nonlinearities i Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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“…Furthermore, all the potential sites for the spontaneous polarization in the crystallite are orthogonal, the gradient of the resultant displacement from switching is a diagonal, uji = u1511 , and is equal to the strain tensor, as given by (2). Thus the work done by the external load in switching the polarization from any initial state to any final state is given by,…”

Section: Idealized Single Crystal Modelmentioning

confidence: 98%

“…The electrical displacement produced during switching is given by (2). Furthermore, all the potential sites for the spontaneous polarization in the crystallite are orthogonal, the gradient of the resultant displacement from switching is a diagonal, uji = u1511 , and is equal to the strain tensor, as given by (2).…”

Section: Idealized Single Crystal Modelmentioning

confidence: 99%

<title>Modeling of nonlinear piezoceramics for structural actuation</title>

Chan

Hagood

1994

SPIE Proceedings

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An ab initio model describing the nonlinear behaviors of polycrystalline piezoceramics during polarization reversal is proposed. The model is based on a description of polarization reversal behaviors of a single piezoelectric crystallite in a piezoceramic. The polarization of the single crystallite can be switched among the six allowable directions in the lattice ifthe work done by the external electrical and/or mechanical loads exceeds the internal energy barriers. The piezoceramic is then modeled as an aggregate of these crystallites rotated into random orientations. The macroscopic responses of the piezoceramic were calculated in two ways. The first method is to calculate the average crystallite response in global coordinates. The second is to use Taylor expansions of the macroscopic strain and electrical displacement in terms of external loads and the internal alignment of the crystallites. Finally, the experimental results from free and clamped PZT wafers were compared with the model predictions.

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A Macroscopic Phenomenological Formulation for Coupled Electromechanical Effects in Piezoelectricity

Cited by 50 publications

References 20 publications

A Free Energy Model for Hysteresis in Ferroelectric Materials

A Free Energy Model for Hysteresis in Ferroelectric Materials

A unified framework for modeling hysteresis in ferroic materials

<title>Modeling of nonlinear piezoceramics for structural actuation</title>

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