Advertisement

Journal of Mechanical Science and Technology

, Volume 32, Issue 11, pp 5273–5277 | Cite as

Constitutive modeling of polarization relaxation behavior in ferroelectrics

  • Kwangsoo Ho
Article

Abstract

A thermodynamically consistent model is formulated to depict the polarization hysteresis and the rate-dependent behavior of relaxation in ferroelectric materials. On the relaxation condition, the polarization gradually changes with time while the applied electric field is kept constant. The present model introduces internal state variables to represent such irreversible dissipation processes. Based on the first and second laws of thermodynamics, the evolution laws of the internal state variables consisting of constitutive equations are then derived through the definitions of the Helmholtz free energy and a dissipation potential. To verify the applicability of the constitutive model, numerical simulations are compared with experiment in the literature.

Keywords

Constitutive model Hysteresis Polarization relaxation Ferroelectric material 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K. Ho, A thermodynamicaaly consistent model for magnetic hysteresis, J. Magn. Magn., 357 (2014) 93–96.CrossRefGoogle Scholar
  2. [2]
    K. Ho, A constitutive model for the frequency dependence of magnetic hysteresis, Physica B, 450 (2014) 143–145.CrossRefGoogle Scholar
  3. [3]
    K. Ho, Thermodynamic formulation of a viscoplastic model capturing unusual loading rate sensitivity, Int. J. Eng. Sci., 100 (2016) 162–170.CrossRefzbMATHGoogle Scholar
  4. [4]
    K. Ho, A constitutive model for magnetostriction based on thermodynamic framework, J. Magn. Magn. Mater., 412 (2016) 250–254.CrossRefGoogle Scholar
  5. [5]
    S. Hwang, C. Lynch and R. McMeeking, Ferroelectric/ferroelastic interactions and a polarization switching model, Acta Metall. Mater., 43 (1995) 2073–2084.CrossRefGoogle Scholar
  6. [6]
    X. Chen, D. Fang and K. Hwang, Micromechanics simulation of ferroelectric polarization switching, Acta Mater., 45 (1997) 3181–3189.CrossRefGoogle Scholar
  7. [7]
    W. Chen and C. S. Lynch, A micro–electro–mechanical model for polarization switching of ferroelectric materials, Acta Mater., 46 (1998) 5303–5311.CrossRefGoogle Scholar
  8. [8]
    J. Huber, N. Fleck, C. Landis and R. McMeeking, A constitutive model for ferroelectric polycrystals, J. Mech. Phys. Solids, 47 (1999) 1663–1697.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    E. Bassiouny, A. Ghaleb and G. Maugin, Thermodynamical formulation for coupled electromechanical hysteresis effects–I. Basic equations, Int. J. Eng. Sci., 26 (1988) 1279–1295.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    H. Tiersten, Electroelastic equations for electroded thin plates subject to large driving voltages, J. Appl. Phys., 74 (1993) 3389–3393.CrossRefGoogle Scholar
  11. [11]
    L. Huang and H. Tiersten, Electroelastic equations describing slow hysteresis in polarized ferroelectric ceramic plates, J. Appl. Phys., 83 (1998) 6126–6139.CrossRefGoogle Scholar
  12. [12]
    M. Kamlah and C. Tsakmakis, Phenomenological modeling of the non–linear electro–mechanical coupling in ferroelectrics, Int. J. Solids Struct., 36 (1999) 669–695.CrossRefzbMATHGoogle Scholar
  13. [13]
    M. Kamlah, Ferroelectric and ferroelastic piezoceramicsmodeling of electromechanical hysteresis phenomena, Contin. Mech. Thermodyn., 13 (2001) 219–268.CrossRefzbMATHGoogle Scholar
  14. [14]
    R. McMeeking and C. Landis, A phenomenological multiaxial constitutive law for switching in polycrystalline ferroelectric ceramics, Int. J. Eng. Sci., 40 (2002) 1553–1577.CrossRefzbMATHGoogle Scholar
  15. [15]
    D. Zhou and M. Kamlah, Determination of roomtemperature creep of soft lead zirconate titanate piezoceramics under static electric fields, J. Appli. Phys., 98 (2005) 104107_1–5.CrossRefGoogle Scholar
  16. [16]
    Q. Liu and J. Huber, Creep in ferroelectrics due to unipolar electrical loading, J. Eur. Ceram. Soc., 26 (2006) 2799–2806.CrossRefGoogle Scholar
  17. [17]
    A. Belov and W. Kreher, Creep in soft PZT: The effect of internal fields, Ferroelectrics, 391 (2009) 12–21.CrossRefGoogle Scholar
  18. [18]
    F. Wolf, A. Sutor, S. Rupitsch and R. Lerch, Modeling and measurement of creep–and rate–dependent hysteresis in ferroelectric actuators, Sensor Actuat. A: Phys., 172 (2011) 245–252.CrossRefGoogle Scholar
  19. [19]
    S. Maniprakash, R. Jayendiran, A. Menzel and A. Arockiarajan, Experimental investigation, modeling and simulation of rate–dependent response of 1–3 ferroelectric composites, Mech. Mater., 94 (2016) 91–105.CrossRefGoogle Scholar
  20. [20]
    B. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal., 13 (1963) 167–178.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    J. Lemaitre and J. Chaboche, Mechanics of solid materials, Cambridge University Press (1990).CrossRefzbMATHGoogle Scholar
  22. [22]
    S. Erlicher and N. Point, Endochronic theory, non–linear kinematic hardening rule and generalized plasticity: A new interpretation based on generalized normality assumption, Int. J. Solids Struct., 43 (2006) 4175–4200.zbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKeimyung UniversityDaeguKorea

Personalised recommendations