A Free Energy Model for Hysteresis in Ferroelectric Materials

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  • Ralph C. Smith
    Department of Methematics
  • Stefan Seelecke
    Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
  • Zoubeida Ounaies
    Department of Mechanical Engineering, Virginia Commonwealth University, Richmond VA 23284-3015, USA
  • Joshua Smith
    Department of Physics, North Carolina State University, Raleigh, NC 27695, USA

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<jats:p> This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques. In the first step of the model development, Helmholtz and Gibbs free energy relations are constructed at the lattice or domain level to quantify the relation between the field and polarization in homogeneous, single crystal compounds which exhibit uniform effective fields. The effects of material nonhomogeneities, polycrystallinity, and variable effective fields are subsequently incorporated through the assumption that certain physical parameters, including the local coercive and effective fields, are randomly distributed and hence manifestations of stochastic density functions associated with the material. Stochastic homogenization in this manner provides low-order macroscopic models with effective parameters that can be correlated with physical properties of the data. This facilitates the identification of parameters for model construction, model updating to accommodate changing operating conditions, and control design utilizing model-based inverse compensators. Attributes of the model, including the guaranteed closure of biased minor loops in quasistatic drive regimes, are illustrated through examples. </jats:p>

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