Skip to main content

Effective Computational Methods for the Modeling of Ferroelectroelastic Hysteresis Behavior

  • Conference paper
  • First Online:

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 24))

Abstract

Numerical methods for the solution of nonlinear electromechanically coupled boundary value problems are considered. A vector potential finite element formulation with return mapping algorithms and consistent tangent operators is developed. The accuracy and robustness of the algorithms are assessed with the help of numerical examples, including a ferroelectroelastic analysis of a notched specimen.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Simo JC, Hughes TJR (1998) Computational inelasticity. Mechanics and materials, vol 7, Springer, New York

    Google Scholar 

  2. Simo JC (1998) Numerical analysis and simulation of plasticity. In: Ciarlet P, Lions J (eds) Handbook of numerical analysis, vol 4. North-Holland, Amsterdam, New York, Oxford, pp 183–499

    Google Scholar 

  3. Semenov AS, Liskowsky AC, Balke H (2010) Return mapping algorithms and consistent tangent operators in ferroelectroelasticity. Int J Numer Methods Eng 81:1298–1340

    MathSciNet  MATH  Google Scholar 

  4. Klinkel S (2006) A phenomenological constitutive model for ferroelastic and ferroelectric hysteresis effects in ferroelectric ceramics. Int J Solids Struct 43:7197–7222

    Article  MATH  Google Scholar 

  5. Kamlah M, Laskewitz B, Zhou D (2007) Ferroelectric ceramics: basic properties and modeling methods. In: Schroeder J, Lupascu D, Balzani D (eds) Proceedings of the 1st seminar on the mechanics of multifunctional materials, Bad Honnef, Germany, pp. 60–63

    Google Scholar 

  6. Simo JC, Taylor RL (1985) Consistent tangent operators for rate-independent elastoplasticity. Comput Methods Appl Mech Eng 48:101–118

    Article  MATH  Google Scholar 

  7. Allik H, Hughes TJR (1970) Finite element method for piezoelectric vibration. Int J Numer Methods Eng 2:151–157

    Article  Google Scholar 

  8. Landis CM (2002) A new finite-element formulation for electromechanical boundary value problems. Int J Numer Methods Eng 55:613–628

    Article  MATH  Google Scholar 

  9. Semenov AS, Kessler H, Liskowsky AC, Balke H (2006) On a vector potential formulation for 3D electromechanical finite element analysis. Commun Numer Methods Eng 22:357–375

    Article  MathSciNet  MATH  Google Scholar 

  10. Landis CM (2002) Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. J Mech Phys Solids 50:127–152

    Article  MATH  Google Scholar 

  11. McMeeking RM, Landis CM (2002) A phenomenological multiaxial constitutive law for switching in polycrystalline ferroelectric ceramics. Int J Eng Sci 40:1553–1577

    Article  MathSciNet  MATH  Google Scholar 

  12. Kantorovich LV, Akilov GP (1964) Functional analysis in normed spaces. Pergamon, Oxford

    MATH  Google Scholar 

  13. Semenov AS (2003) PANTOCRATOR – the finite element program specialized on the nonlinear problem solution. In: Melnikov BE (ed) Proceedings of the Vth international conference on scientific and engineering problems of predicting the reliability and service life of structures, St.-Petersburg, pp. 466–480

    Google Scholar 

  14. Jelitto H, Kessler H, Schneider GA, Balke H (2005) Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads. J Eur Ceram Soc 25:749–757

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful for the support of this work by the DFG.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Artem S. Semenov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this paper

Cite this paper

Semenov, A.S., Liskowsky, A.C., Neumeister, P., Balke, H. (2011). Effective Computational Methods for the Modeling of Ferroelectroelastic Hysteresis Behavior. In: Kuna, M., Ricoeur, A. (eds) IUTAM Symposium on Multiscale Modelling of Fatigue, Damage and Fracture in Smart Materials. IUTAM Bookseries, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9887-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9887-0_5

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9886-3

  • Online ISBN: 978-90-481-9887-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics