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A Phenomenological Constitutive Model for Ferroelectric Ceramics and Ferromagnetic Materials

  • Sven Klinkel
  • Konrad Linnemann
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 24)

Abstract

This Contribution is concerned with a macroscopic nonlinear constitutive law for ferromagnetic alloys and ferroelectric ceramics. It accounts for the hysteresis effects which occur in the considered class of materials. The uniaxial model is thermodynamically motivated and based on the definition of a specific free energy function and a switching criterion. The strains and the magnetic or electric field strength are additively split into a reversible and an irreversible part. Analogous to plasticity, the irreversible quantities serve as internal variables. A one-to-one-relation between the two internal variables provides conservation of volume during polarization or magnetization process. The material model is able to approximate the ferromagnetic or ferroelectric hysteresis curves and the related butterfly hysteresis curves. An extended approach for ferrimagnetic behavior which occurs in ferromagnetic materials is presented. A main aspect of the constitutive model is its numerical treatment. The model is embedded in a three dimensional finite element formulation. The usage of the irreversible field strength permits the application of algorithms known from the treatment of computational inelasticity.

Keywords

Constitutive Model Internal Variable Hysteresis Curve Ferroelectric Ceramic Free Energy Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Carman GP, Mitrovic M (1995) Nonlinear constitutive relations for magnetostrictive materials with applications to 1-d problems. J Int Mat Sys Struc 6(5):673–683CrossRefGoogle Scholar
  2. 2.
    Dapino MJ, Flatau AB, Calkins FT (2006) Statistical analysis of terfenol-d material properties. J Int Mat Sys Struc 17(7):587–599CrossRefGoogle Scholar
  3. 3.
    Engdahl G (2000) Handbook of giant magnetostrictive materials. Academic, San DiegoGoogle Scholar
  4. 4.
    Fang DN, Feng X, Hwang KC (2004) Study of magnetomechanical non-linear deformation of ferromagnetic materials: Theory and experiment. Proc Inst Mech Eng Part C J Mech Eng Sci 218(12):1405–1410CrossRefGoogle Scholar
  5. 5.
    Hwang SC, Lynch CS, McMeeking RM (1995) Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metal Mater 43(5):2073–2084CrossRefGoogle Scholar
  6. 6.
    Kamlah M Ferroelectric and ferroelastic piezoceramics – Modeling of electromechanical hysteresis phenomena. Continuum Mech Thermodyn 13:219–268Google Scholar
  7. 7.
    Klinkel S (2006) A phenomenological constitutive model for ferroelastic and ferroelectric hysteresis effects in ferroelectric ceramics. Int J Solid Struct 43(22–23):7197–7222zbMATHCrossRefGoogle Scholar
  8. 8.
    Landis CM (2002) Fully coupled multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. J Mech Phys Solid 50:127–152zbMATHCrossRefGoogle Scholar
  9. 9.
    Linnemann K, Klinkel S, Wagner W (2009) A constitutive model for magnetostrictive and piezoelectric materials. Int J Solid Struct 46:1149–1166zbMATHCrossRefGoogle Scholar
  10. 10.
    McMeeking RM, Landis CM (2002) A phenomenological multi-axial constitutive switching in polycrystalline ferroelectric ceramics. Int J Eng Sci 40:1553–1577MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Mehling V, Tsakmakis Ch, Gross D (2007) Phenomenological model for the macroscopic material behavior of ferroelectric ceramics. Int J Mech Phys Solids 55:2106–2141MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Smith RC, Dapino MJ, Seelecke S (2003) Free energy model for hysteresis in magnetostrictive transducers. J Appl Phys 93(1):458–466CrossRefGoogle Scholar
  13. 13.
    Wan YP, Fang DN, Hwang KC (2003) Non-linear constitutive relations for magnetostrictive materials. Int J Non-Linear Mech 38(7):1053–1065zbMATHCrossRefGoogle Scholar
  14. 14.
    Zheng XJ, Sun L (2007) A one-dimension coupled hysteresis model for giant magnetostrictive materials. J Magnet Magnet Mater 309(2):263–271MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zheng XJ, Liu XE (2005) A nonlinear constitutive model for terfenol-d rods. J Appl Phys 97(5):053901CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Statik und Dynamik der TragwerkeTU KaiserslauternKaiserslauternGermany
  2. 2.Institut für BaustatikUniversität Karlsruhe (TH)KarlsruheGermany

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