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

Bartel, T. ; Schulte, R. ; Menzel, A. LU ; Kiefer, B. and Svendsen, B. (2019) In Archive of Applied Mechanics 89(6). p.995-1010
Abstract

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... (More)

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.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convergence studies, Ferroelectrics, Fischer–Burmeister NCP functions, Laminate-based material model
in
Archive of Applied Mechanics
volume
89
issue
6
pages
995 - 1010
publisher
Springer
external identifiers
  • scopus:85053528168
ISSN
0939-1533
DOI
10.1007/s00419-018-1466-7
language
English
LU publication?
yes
id
4c253b12-0d15-4f10-ad0d-f4f3326f7511
date added to LUP
2018-10-23 10:59:23
date last changed
2020-10-07 06:06:11
@article{4c253b12-0d15-4f10-ad0d-f4f3326f7511,
  abstract     = {<p>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.</p>},
  author       = {Bartel, T. and Schulte, R. and Menzel, A. and Kiefer, B. and Svendsen, B.},
  issn         = {0939-1533},
  language     = {eng},
  number       = {6},
  pages        = {995--1010},
  publisher    = {Springer},
  series       = {Archive of Applied Mechanics},
  title        = {Investigations on enhanced Fischer–Burmeister NCP functions : application to a rate-dependent model for ferroelectrics},
  url          = {http://dx.doi.org/10.1007/s00419-018-1466-7},
  doi          = {10.1007/s00419-018-1466-7},
  volume       = {89},
  year         = {2019},
}