Multiscale Characterization and Model for the Dynamic Behavior of Ferroelectric Materials Using Fractional Operators

  • Benjamin DucharneEmail author
  • Grzegorz Litak
  • Bin Zhang
  • Bhaawan Gupta
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 24)


Fractional operators are well adapted to model dynamic dielectric losses of ferroelectric materials. Where usual integer derivative operators are always limited to a relatively weak frequency bandwidth, an approach based on fractional derivatives provides good simulation results even beyond working frequency of industrial systems. In this article, we determined the link between a high excitation (> 2 kV/mm), weak frequency (< 100 Hz) dynamic dielectric fractional hysteresis model and the weak excitation stress level (< 5 V/mm) but large frequency bandwidth (40 Hz < f < 40 MHz) well known as dielectric permittivity fractional models (Cole-Cole model and Havriliak-Negami). The good comparison of simulation/measure was obtained considering the same sample and the same dynamic parameters (fractional order together with nonlinear dry friction parametrization) in both cases. This allows attributing the same physical origin of the dielectric losses simulated here (the dielectric relaxation). Furthermore it is also possible to limit the ferroelectric dynamic characterization with the impedance analyzer measure (where all the model parameters can be set) and to anticipate the high electrical amplitude stress behavior in simulation.


Cole-Cole Model Hysteresis Model Impedance Analyzer Measure Large Frequency Bandwidth Fractional Derivative 
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The authors would like to thank for the support from the Polish-French collaboration project (Polonium).


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Benjamin Ducharne
    • 1
    Email author
  • Grzegorz Litak
    • 1
    • 2
    • 3
  • Bin Zhang
    • 4
  • Bhaawan Gupta
    • 1
    • 5
  1. 1.Laboratoire de Genie Electrique et FerroelectriciteInstitut National des Sciences Appliquees de LyonVilleurbanneFrance
  2. 2.Faculty of Mechanical EngineeringLublin University of TechnologyLublinPoland
  3. 3.Department of Process ControlAGH University of Science and TechnologyKrakówPoland
  4. 4.Reseach Center of Mechanics and Mechatronic EquipmentShandong UniversityWeihaiChina
  5. 5.ELYTLABTOHOKU UniversitySendaïJapan

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