A homogenized free energy model for hysteresis in thin-film shape memory alloys

Massad, Jordan Elias; Smith, Ralph C.

doi:10.1016/j.tsf.2005.04.079

“…The homogenized energy model developed in [11,16,18,20] provides a unified framework for characterizing hysteresis and constitutive nonlinearities in ferroelectric, ferromagnetic and ferroelastic materials. Due to the energy formulation of the framework, the effects of thermally activated relaxation phenomenon, stress-dependence and thermal dependence can be incorporated in a natural manner.…”

Section: Discussionmentioning

confidence: 99%

“…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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“…The kernel development for the stress-dependent case is analogous but employs the Gibbs relation (11). Due to the definition (7) in the Helmholtz energy, 4 switching points occur: from either positive or negative to 90 o and from 90 o to either 180 o orientation.…”

Section: Stress-dependent Regimes: 180 O and 90 O Switchingmentioning

confidence: 99%

Efficient Implementation Algorithms for Homogenized Energy Models

Braun

¹

,

Smith

²

2006

Continuum Mech. Thermodyn.

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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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“…In the manner detailed in Section 4.1.3, thermal activation processes are incorporated through the use of the Boltzmann relation (14). For the 1-D model, the polarization has three allowed dipole states P − , P + and P 90 .…”

Section: Switching In the Presence Of Thermal Activationmentioning

confidence: 99%

A Stress-Dependent Hysteresis Model for Ferroelectric Materials

Ball¹,

Smith²,

Kim³

et al. 2005

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This paper addresses the development of homogenized energy models which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 • and 180 • dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data. 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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A homogenized free energy model for hysteresis in thin-film shape memory alloys

Cited by 36 publications

References 109 publications

Efficient Implementation Algorithms for Homogenized Energy Models

Efficient Implementation Algorithms for Homogenized Energy Models

Efficient Implementation Algorithms for Homogenized Energy Models

A Stress-Dependent Hysteresis Model for Ferroelectric Materials

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