A unified framework for modeling hysteresis in ferroic materials

Smith, Ralph C.; Seelecke, Stefan; Dapino, Marcelo J.; Ounaies, Zoubeida

doi:10.1016/j.jmps.2005.08.006

“…domain wall models [7,10,17], Preisach models [5,12,13,21], and homogenized energy models [11,15,16,18,20]. Whereas certain facets of relaxation and stress-dependence have been incorporated in domain wall models and Preisach models -e.g., [4] and [6] -comprehensive theory incorporating these mechanisms for general compounds has not been developed within these two frameworks.…”

Section: Homogenized Energy Frameworkmentioning

confidence: 99%

Efficient Implementation Algorithms for Homogenized Energy Models

Braun¹,

Smith²

2005

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The homogenized energy framework quantifying ferroelectric and ferromagnetic hysteresis is increasingly used for comprehensive material characterization and model-based control design. For operating regimes in which thermal relaxation mechanisms and stress-dependencies are negligible, existing algorithms are sufficiently efficient to permit device optimization and the potential for real-time control implementation. In this paper, we develop algorithms employing lookup tables which permit the high speed implementation of formulations which incorporate relaxation mechanisms and electromechanical coupling. Aspects of the algorithms are illustrated through comparison with experimental data. Homogenized Energy FrameworkFerroelectric and ferromagnetic materials are being considered as transducers for an increasing number of applications due to their broadband capabilities, large electromechanical and magnetomechanical coupling factors, and their dual capability for actuating and sensing. At low drive levels, the direct and converse electromechanical/magnetomechanical effects are approximately linear, and linear models and control designs can be employed. However, at the moderate to high drive levels where the unique transducer capabilities are manifested, the constitutive material properties are inherently nonlinear and hysteretic. Material characterization necessitates the development of models which accurately characterize constitutive nonlinearities and hysteresis whereas device optimization and real-time control implementation requires that the models be highly efficient to implement. While a number of frameworks have been developed for characterizing ferroelectric and ferromagnetic hysteresis, the competing requirements of accuracy and efficiency limit which models may be considered for both material characterization and real-time implementation.At the microscopic scale, the physical mechanisms which produce hysteresis in ferroelectric and ferromagnetic materials differ substantially since ferroelectricity is due to the ionic structure of materials and ferromagnetism results from interactions between magnetic moments and electron spins. However, at the domain or macroscopic scale, shared physical and energy properties permit the development of unified frameworks for characterizing hysteresis of compounds (see [14] for details regarding shared properties of ferroic materials at the various scales).In addition to the dielectric and magnetic hysteresis exhibited by the compounds, transducer models must characterize the thermal relaxation effects and stress-dependencies exhibited by ferroelectric and ferromagnetic materials. The former phenomenon is illustrated in Figure 1(a) with magnetic data collected from a steel rod [3]. Stress effects are illustrated in Figure 1(b) via PLZT data from [9].As detailed in [14], several frameworks have been developed to characterize ferroelectric and ferromagnetic hysteresis for regimes in which relaxation mechanisms and stress-dependencies are negligible. These include *

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“…We note that a significant advantage of the energy-based model is the fact that it provides a unified framework for characterizing hysteresis and constitutive nonlinearities in ferroelectric, ferromagnetic and ferroelastic (e.g., SMA) compounds [28,29]. One facet of present investigations focuses on the extension and implementation of the inverse filtering techniques for the latter two classes of compounds.…”

Section: Discussionmentioning

confidence: 99%

“…Numerous approaches have been employed to characterize these nonlinear effects including Preisach models [7,18], domain wall models [25,26], micromechanical models [4,10,11], mesoscopic energy relations [3,9] and homogenized energy models [23,30]. We employ the homogenized energy framework due to its energy basis, its capability to quantify a wide range of physical phenomena and operating regimes, its unified nature for characterizing hysteresis in ferroelectric, ferromagnetic and ferroelastic compounds [28,29], and the potential it provides for real-time implementation. Details regarding the development of this modeling framework and its relation to other characterization techniques can be found in [21,30].…”

Section: Introductionmentioning

confidence: 99%

Construction and Experimental Implementation of a Model-Based Inverse Filter to Attenuate Hysteresis in Ferroelectric Transducers

Hatch¹,

Smith²,

De³

et al. 2005

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Hysteresis and constitutive nonlinearities are inherent properties of ferroelectric transducer materials due to the noncentrosymmetric nature of the compounds. In certain regimes, these effects can be mitigated through restricted input fields, charge-or current-controlled amplifiers, or feedback designs. For general operating conditions, however, these properties must be accommodated in models, transducer designs, and model-based control algorithms to achieve the novel capabilities provided by the compounds. In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear design and control implementation. Attributes of the inverse filters are illustrated through numerical examples and experimental open loop control implementation for an atomic force microscope stage.i Report Documentation Page Form Approved OMB No. 0704-0188Public 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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“…Thus, the values associated with each exp and erfc evaluation are bounded and this bound can be determined a priori. This defines the lookup table approach; before running the algorithm, the range between each input is discretized, and the values of (17) and (19) are computed and stored for every grid element. With even a moderate number of time steps, this reduces the overall computational effort; however, the # Initial Setup -to be done in advance addit = N c −1…”

Section: Algorithm For Thermal Relaxation Stress-invariant Regimesmentioning

confidence: 99%

Efficient Implementation Algorithms for Homogenized Energy Models

Braun

¹

,

Smith

²

2006

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

The homogenized energy framework quantifying ferroelectric and ferromagnetic hysteresis is increasingly used for comprehensive material characterization and model-based control design. For operating regimes in which thermal relaxation mechanisms and stress-dependencies are negligible, existing algorithms are sufficiently efficient to permit device optimization and the potential for real-time control implementation. In this paper, we develop algorithms employing lookup tables which permit the high speed implementation of formulations which incorporate relaxation mechanisms and electromechanical coupling. Aspects of the algorithms are illustrated through comparison with experimental data. Homogenized Energy FrameworkFerroelectric and ferromagnetic materials are being considered as transducers for an increasing number of applications due to their broadband capabilities, large electromechanical and magnetomechanical coupling factors, and their dual capability for actuating and sensing. At low drive levels, the direct and converse electromechanical/magnetomechanical effects are approximately linear, and linear models and control designs can be employed. However, at the moderate to high drive levels where the unique transducer capabilities are manifested, the constitutive material properties are inherently nonlinear and hysteretic. Material characterization necessitates the development of models which accurately characterize constitutive nonlinearities and hysteresis whereas device optimization and real-time control implementation requires that the models be highly efficient to implement. While a number of frameworks have been developed for characterizing ferroelectric and ferromagnetic hysteresis, the competing requirements of accuracy and efficiency limit which models may be considered for both material characterization and real-time implementation.At the microscopic scale, the physical mechanisms which produce hysteresis in ferroelectric and ferromagnetic materials differ substantially since ferroelectricity is due to the ionic structure of materials and ferromagnetism results from interactions between magnetic moments and electron spins. However, at the domain or macroscopic scale, shared physical and energy properties permit the development of unified frameworks for characterizing hysteresis of compounds (see [14] for details regarding shared properties of ferroic materials at the various scales).In addition to the dielectric and magnetic hysteresis exhibited by the compounds, transducer models must characterize the thermal relaxation effects and stress-dependencies exhibited by ferroelectric and ferromagnetic materials. The former phenomenon is illustrated in Figure 1(a) with magnetic data collected from a steel rod [3]. Stress effects are illustrated in Figure 1(b) via PLZT data from [9].As detailed in [14], several frameworks have been developed to characterize ferroelectric and ferromagnetic hysteresis for regimes in which relaxation mechanisms and stress-dependencies are negligible. These include *

show abstract

A unified framework for modeling hysteresis in ferroic materials

Cited by 99 publications

References 107 publications

Efficient Implementation Algorithms for Homogenized Energy Models

Efficient Implementation Algorithms for Homogenized Energy Models

Construction and Experimental Implementation of a Model-Based Inverse Filter to Attenuate Hysteresis in Ferroelectric Transducers

Efficient Implementation Algorithms for Homogenized Energy Models

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