A homogenized energy framework for ferromagnetic hysteresis

Smith, Ralph C.; Dapino, Marcelo J.

doi:10.1109/tmag.2006.875717

Cited by 73 publications

(91 citation statements)

References 72 publications

(161 reference statements)

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“…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%

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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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Section: Homogenized Energy Frameworkmentioning

confidence: 99%

“…To incorporate thermal activation, we again balance (11) with relative thermal energy via the Boltzmann relation (15). This yields three average polarization relations…”

Section: Stress-dependent Regimes: 180mentioning

confidence: 99%

Efficient Implementation Algorithms for Homogenized Energy Models

Braun¹,

Smith²

2005

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“…The nonlinear and hysteretic material modeling summarized here is based on a stochastic homogenized energy model which is based on previous work described in detail in [5][6][7][8][9][10]. Here, only key equations are given to motivate the implementation of the constitutive model in the structural dynamic model and control design.…”

Section: Model Developmentmentioning

confidence: 99%

Open loop nonlinear optimal tracking control of a magnetostrictive terfenol-D actuator

Oates

Evans

Smith

et al. 2007

Behavior and Mechanics of Multifunctional and Composite Materials 2007

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A homogenized energy model was implemented in a model-based nonlinear control design to accurately track a reference displacement signal for high frequency magnetostrictive actuator applications. Rate dependent nonlinear and hysteretic magnetostrictive constitutive behavior is incorporated into the finite-dimensional optimal control design to improve control at high frequency. The integration of the rate-dependent nonlinear and hysteretic magnetostrictive constitutive model in the control design minimized the amount of feedback required for precision control. The control design is validated experimentally and shown to accurately track a reference signal at frequencies up to at least 1 kHz.

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“…Experimental validation for operating regimes in which magnetic after-effects are negligible are also provided in therein. In this letter, we illustrate the ability of the model to quantify after-effects through fits of experimental steel data.As detailed in [3][4][5], the macroscopic magnetization is quantified by the relationin the homogenized energy framework. Here, ν1 and ν2 denote the densities for the local coercive field Hc and interaction field HI .…”

mentioning

confidence: 99%

“…The effects of polycrystallinity, material nonhomogeneities, and variable interaction fields are subsequently incorporated by assuming that local coercive and interaction fields are manifestations of underlying distributions rather than constant coefficients. The development of this framework is provided in [3][4][5]. Experimental validation for operating regimes in which magnetic after-effects are negligible are also provided in therein.…”

mentioning

confidence: 99%

Experimental validation of a homogenized energy model for magnetic after-effects

Braun

Smith

Dapino

2006

Applied Physics Letters

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In this letter, we experimentally validate the ability of a recently developed ferromagnetic hysteresis model to characterize magnetic after-effects in ferromagnetic materials. The modeling framework, which combines energy analysis at the lattice level with stochastic homogenization techniques to accommodate material, stress and field nonhomogeneities, quantifies after-effects through a balance of the Gibbs and relative thermal energies. Attributes of the framework are illustrated through fits to experimental steel data.Magnetic after-effects due to either thermally-induced switching or atomic diffusion produce drift or creep in the magnetization or induction for a number of operating regimes [1; 2]. Quantification of these effects is important both for accurate material characterization and the design of sensors and actuators required to achieve and maintain highly accurate tolerances.In a recently developed framework for quantifying hysteresis inherent to ferromagnetic materials, magnetic after-effects are incorporated by balancing the Gibbs and relative thermal energies at the lattice level using Boltzmann principles. The effects of polycrystallinity, material nonhomogeneities, and variable interaction fields are subsequently incorporated by assuming that local coercive and interaction fields are manifestations of underlying distributions rather than constant coefficients. The development of this framework is provided in [3][4][5]. Experimental validation for operating regimes in which magnetic after-effects are negligible are also provided in therein. In this letter, we illustrate the ability of the model to quantify after-effects through fits of experimental steel data.As detailed in [3][4][5], the macroscopic magnetization is quantified by the relationin the homogenized energy framework. Here, ν1 and ν2 denote the densities for the local coercive field Hc and interaction field HI . The abscissas associated with the quadrature formula under consideration are denoted by HI j , Hc i and the quadrature weights are given by vi, wj. To construct the model, one can treat the density values {ν1(Hc i ), ν2(HI

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A homogenized energy framework for ferromagnetic hysteresis

Cited by 73 publications

References 72 publications

Efficient Implementation Algorithms for Homogenized Energy Models

Efficient Implementation Algorithms for Homogenized Energy Models

Open loop nonlinear optimal tracking control of a magnetostrictive terfenol-D actuator

Experimental validation of a homogenized energy model for magnetic after-effects

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