Investigations on enhanced Fischer–Burmeister NCP functions: application to a rate-dependent model for ferroelectrics

  • T. BartelEmail author
  • R. Schulte
  • A. Menzel
  • B. Kiefer
  • B. Svendsen


This contribution deals with investigations on enhanced Fischer–Burmeister nonlinear complementarity problem (NCP) functions applied to a rate-dependent laminate-based material model for ferroelectrics. The framework is based on the modelling and parametrisation of the material’s microstructure via laminates together with the respective volume fractions. These volume fractions are treated as internal-state variables and are subject to several inequality constraints which can be treated in terms of Karush–Kuhn–Tucker conditions. The Fischer–Burmeister NCP function provides a sophisticated scheme to incorporate Karush–Kuhn–Tucker-type conditions into calculations of internal-state variables. However, these functions are prone to numerical instabilities in their original form. Therefore, some enhanced formulations of the Fischer–Burmeister ansatz are discussed and compared to each other in this contribution.


Fischer–Burmeister NCP functions Convergence studies Ferroelectrics Laminate-based material model 



The financial support of the German Research Foundation (DFG) of the research group FOR 1509, “Ferroic Functional Materials: Multi-scale Modeling and Experimental Characterization” in projects P6 “Microstructural Interactions and Switching in Ferroelectrics” and P7 “Numerical Relaxation Techniques for the Modeling of Microstructure Evolution in Multifunctional Magnetic Materials” is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • T. Bartel
    • 1
    Email author
  • R. Schulte
    • 1
  • A. Menzel
    • 1
    • 2
  • B. Kiefer
    • 3
  • B. Svendsen
    • 4
    • 5
  1. 1.Institue of MechanicsTU DortmundDortmundGermany
  2. 2.Division of Solid MechanicsLund UniversityLundSweden
  3. 3.Institute of Mechanics and Fluid DynamicsTU Bergakademie FreibergFreibergGermany
  4. 4.Chair of Material MechanicsRWTH AachenAachenGermany
  5. 5.Microstructure Physics and Alloy DesignMax-Planck-Institut fuer Eisenforschung GmbHDuesseldorfGermany

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