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Finite Element Simulation of the Non-remanent Straining Ferroelectric Material Behaviour Based on the Electrostatic Scalar Potential:Convergence and Stability

  • Stephan Roth
  • Peter Neumeister
  • Artem S. Semenov
  • Herbert Balke
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 24)

Abstract

The applicability of the Newton–Raphson iteration scheme to an electric scalar potential formulation of a ferroelectric/ferroelastic constitutive model within the framework of a finite element simulation is analysed methodically. Since the specific shape of the polarisation hysteresis is recognised as the principal reason of numerical problems, the considerations given here are limited to the non-remanent straining ferroelectric material model. Three approaches to gain convergence are discussed. Besides the known Line Search two other methods are presented, which are applied locally for each integration point. While the main idea of the first is to modify the vector of the internal dielectric displacement, the second approach affects the tangent modulus. An additional scaling of the tangent modulus is proposed in order to suppress numerical instabilities which may arise as a consequence of an over-compensation of numerical errors. To identify the remanent polarisation an enhanced Return Mapping algorithm based on an implicit backward Euler method is used. The applicability of the modified numerical iteration procedure is demonstrated by two examples.

Keywords

Tangent Modulus Raphson Method Remanent Polarisation Switching Surface Maximum Relative Deviation 
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.

Notes

Acknowledgements

The authors greatly acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG) under Contract No. Ba 1411/12.

References

  1. 1.
    Belytschko T (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkzbMATHGoogle Scholar
  2. 2.
    Huber JE, Fleck NA (2001) Multi-axial electrical switching of a ferroelectric: Theory versus experiment. J Mech Phys Solids 49:785–811zbMATHCrossRefGoogle Scholar
  3. 3.
    Landis CM (2002) Fully coupled multi-axial, symmetric constitutive laws for polycristalline ferroelectric ceramics. J Mech Phys Solids 50:127–152 (2002)zbMATHCrossRefGoogle Scholar
  4. 4.
    Nakata T, et al (1992) Improvements of convergence characteristics of newton-raphson method for nonlinear magnetic field analysis. IEEE Trans Magn 28(2):1048–1051CrossRefGoogle Scholar
  5. 5.
    Semenov AS, Kessler H, Liskowsky AC, Balke H (2006) On a vector potential formulation for 3d electromechanical finite element analysis. Commun Num Meth Eng 22:357–375MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Semenov AS, Liskowsky AC, Balke H (2010) Return mapping algorithms and consistent tangent operators in ferroelectroelasticity. Int J Num Meth Eng 81(10):1298–1340MathSciNetzbMATHGoogle Scholar
  7. 7.
    Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Stephan Roth
    • 1
  • Peter Neumeister
    • 2
  • Artem S. Semenov
    • 2
  • Herbert Balke
    • 2
  1. 1.Institute of Mechanics and Fluid DynamicsTU Bergakademie FreibergFreibergGermany
  2. 2.Fakultät MaschinenwesenTechnische Universität DresdenDresdenGermany

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