A Free Energy Model for Hysteresis in Ferroelectric Materials

Ralph C. Smith, Stefan Seelecke, Zoubeida Ounaies, Joshua Smith

Research output: Contribution to journalArticle

100 Citations (Scopus)

Abstract

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 controldesign 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.

Original languageEnglish (US)
Pages (from-to)719-739
Number of pages21
JournalJournal of Intelligent Material Systems and Structures
Volume14
Issue number11
DOIs
StatePublished - Nov 1 2003

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Free energy
Ferroelectric materials
Hysteresis
Control nonlinearities
Gibbs free energy
Probability density function
Identification (control systems)
Physical properties
Single crystals
Polarization

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanical Engineering

Cite this

Smith, Ralph C. ; Seelecke, Stefan ; Ounaies, Zoubeida ; Smith, Joshua. / A Free Energy Model for Hysteresis in Ferroelectric Materials. In: Journal of Intelligent Material Systems and Structures. 2003 ; Vol. 14, No. 11. pp. 719-739.
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A Free Energy Model for Hysteresis in Ferroelectric Materials. / Smith, Ralph C.; Seelecke, Stefan; Ounaies, Zoubeida; Smith, Joshua.

In: Journal of Intelligent Material Systems and Structures, Vol. 14, No. 11, 01.11.2003, p. 719-739.

Research output: Contribution to journalArticle

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