Hysteresis Parameter Identification With Limited Experimental Data

Iyer, Ram; Shirley, Matthew Edward

doi:10.1109/tmag.2004.833427

Cited by 66 publications

(41 citation statements)

References 21 publications

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“…For a detailed description and a discussion regarding the choice of the Preisach function see e.g. References [49,50,47,51]. It is remarked that the polarization output value denotes the normalized irreversible polarization.…”

Section: Interpretation For Ferroelectric Materialsmentioning

confidence: 99%

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A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

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In this paper we present a nonlinear finite element formulation for piezoelectric shell structures. Based on a mixed multi field variational formulation, an electro-mechanical coupled shell element is developed considering geometrically and materially nonlinear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference of the electric potential in thickness direction of the shell. Incorporating nonlinear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner-Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three-dimensional transversal isotropic material law, thus the kinematic in thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and resultant dielectric displacement fields. Accounting for material nonlinearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperaturedependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature dependent hysteresis curves.

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Section: Interpretation For Ferroelectric Materialsmentioning

confidence: 99%

“…We solve the integrals in (50) and (66) numerically with a 2 × 2 Gauss scheme. By means of the element matrices, the linearized variational formulation of equation (65) can be simplified as…”

Section: [16]mentioning

confidence: 99%

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

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“…Phenomenological models, on the other hand, aim only to approximate the physics, thus giving simpler models. The Preisach operator model Iyer and Tan (2009); Hughes and Wen (1997); Iyer and Shirley (2004); Tan et al (2001); Tan and Baras (2005); Leang and Devasia (2006); Zhao and Tan (2006) for hysteresis modelling was first regarded as a physical model for hysteresis based on some hypothesis concerning the physical mechanisms of magnetization Mayergoyz (2003) the model has been recognized as a phenomenologicalbased model mainly due to a more general description. The idea of Preisach models, including the Preisach operator, the Krasnosel'skii-Pokrovskii (KP) operator Riccardi et al (2012); Tan and Bennani (2008) and the Prandtl-Ishlinskii (PI) operator Al Janaideh et al (2011); Macki et al (1993) is to calculate an output as a sum of weighted basis operators.…”

Section: Introductionmentioning

confidence: 99%

“…However this method involves differentiation of a measurement, and will consequently be highly sensitive to measurement noise. The most common method for identification of the Preisach density function is based on the constrained least squares method Iyer and Tan (2009);Iyer and Shirley (2004); Galinaitis et al (2001);Tan (2002);Eielsen (2012). In contrast to linear systems, hysteresis is a rate-independent effect, i.e.…”

Section: Introductionmentioning

confidence: 99%

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On Implementation of the Preisach Model: Identification and Inversion for Hysteresis Compensation

Stakvik¹,

Ragazzon²,

Eielsen³

et al. 2015

MIC

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A challenge for precise positioning in nanopositioning using smart materials is hysteresis, limiting positioning accuracy. The Preisach model, based on the delayed relay operator for hysteresis modelling, is introduced. The model is identified from experimental data with an input function ensuring information for all input levels. This paper presents implementational issues with respect to hysteresis compensation using the Preisach model, showing the procedure to follow, avoiding pitfalls in both identification and inversion. Issues due to the discrete nature of the Preisach model are discussed, and a specific linear interpolation method is tested experimentally, showing effective avoidance of excitation of vibrational dynamics in the smart material. Experimental results of hysteresis compensation are presented, showing an approximate error of 5% between the reference and measured displacement. Consequences of an insufficient discretization level and a high frequency reference signal are illustrated, showing significant deterioration of the hysteresis compensation performance.

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A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

Butz

Klinkel

Wagner

2008

Numerical Meth Engineering

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This paper is concerned with a three-dimensional piezoelectric beam formulation and its finite element implementation. The developed model considers geometrically and materially non-linear effects. Ail eccentric beam formulation is derived based on the Timoshenko kinematics. The kinematic assumptions are extended by three additional warping functions of the cross section. These functions follow from torsion and piezoelectrically induced shear deformations. The presented beam formulation incorporates large displacements and finite rotations and allows the investigation of stability problems. The finite element model has two nodes with nine mechanical and five electrical degrees of freedom. It provides ail accurate approximation of the electric potential, which is assumed to be linear in the direction of the beam axis and quadratic within the cross section. The mechanical degrees of freedom are three displacements, three rotations and three scaling factors for the warping functions. The latter are computed in a preprocess by solving a two-dimensional in-plane equilibrium condition with the finite element method. The gained warping patterns are considered within the integration through the cross section of the beam formulation. With respect to material non-linearities, which arise in ferroelectric materials, the scalar Preisach model is embedded in the formulation. This model is a mathematical model for the general description of hysteresis phenomena. Its application to piezoelectric materials leads to a phenomenological model for ferroelectric hysteresis effects. Here, the polarization direction is assumed to be constant, which leads to unidirectional constitutive equations. Some examples demonstrate the capability of the proposed model

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Hysteresis Parameter Identification With Limited Experimental Data

Cited by 66 publications

References 21 publications

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

On Implementation of the Preisach Model: Identification and Inversion for Hysteresis Compensation

A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

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