A Homogenized Energy Model for Hysteresis in Ferroelectric Materials: General Density Formulation

Abstract

In this paper, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations which can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data.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.

Experimental implementation of a model-based inverse filter to attenuate hysteresis in an atomic force microscope

“…The latter involves the quantification of both thermal relaxation and inertial effects as illustrated by the change in sign of the slope ∂P ∂E following field reversal. Further details demonstrating properties of the model for characterizing hysteresis in various PZT compounds can be found in [6,8,10]. …”

“…In both cases, displacements were computed using the ODE model constructed using the stress relation (17) and hysteresis model (14) with general densities ν 1 and ν 2 identified using the techniques detailed in [6,8]. Figure 4 demonstrates the characterization of frequency dependent dynamics.…”

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

“…Techniques for identifying the densities ν 1 and ν 2 are illustrated in [23]. For certain applications, reasonable accuracy is provided by a priori functions satisfying the physical criteria (12) and having a small number of parameters to be estimated through least squares fits to data -e.g., variances and means in normal and lognormal relations.…”

“…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.…”

Experimental Study on the Electromechanical Hysteresis Property of Macro Fibre Composite Actuator

“…12 The former models, like Jiles-Atherton model 13 and homogenized energy model, 14 are formulated based on the physical principle of domain wall movements and internal energy losses in the material. Nevertheless, these physical models are difficult to be applied in control system due to the complex physical cause of hysteresis phenomenon of piezoelectric actuator.…”