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Simulation of magnetised microstructure evolution based on a micromagnetics-inspired FE framework : application to magnetic shape memory behaviour

Buckmann, Karsten; Kiefer, Björn; Bartel, Thorsten and Menzel, Andreas LU (2019) In Archive of Applied Mechanics 89(6). p.1085-1102
Abstract

Microstructure evolution in magnetic materials is typically a non-local effect, in the sense that the behaviour at a material point depends on the magnetostatic energy stored within the demagnetisation field in the entire domain. To account for this, we propose a finite element framework in which the internal state variables parameterising the magnetic and crystallographic microstructure are treated as global fields, optimising a global potential. Contrary to conventional micromagnetics, however, the microscale is not spatially resolved and exchange energy terms are neglected in this approach. The influence of microstructure evolution is rather incorporated in an effective manner, which allows the computation of meso- and macroscale... (More)

Microstructure evolution in magnetic materials is typically a non-local effect, in the sense that the behaviour at a material point depends on the magnetostatic energy stored within the demagnetisation field in the entire domain. To account for this, we propose a finite element framework in which the internal state variables parameterising the magnetic and crystallographic microstructure are treated as global fields, optimising a global potential. Contrary to conventional micromagnetics, however, the microscale is not spatially resolved and exchange energy terms are neglected in this approach. The influence of microstructure evolution is rather incorporated in an effective manner, which allows the computation of meso- and macroscale problems. This approach necessitates the development and implementation of novel mixed finite element formulations. It further requires the enforcement of inequality constraints at the global level. To handle the latter, we employ Fischer–Burmeister complementarity functions and introduce the associated Lagrange multipliers as additional nodal degrees-of-freedom. As a particular application of this general methodology, a recently established energy-relaxation-based model for magnetic shape memory behaviour is implemented and tested. Special cases—including ellipsoidal specimen geometries—are used to verify the magnetisation and field-induced strain responses obtained from finite element simulations by comparison to calculations based on the demagnetisation factor concept.

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author
organization
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type
Contribution to journal
publication status
published
subject
keywords
Magnetic shape memory alloys, Magnetostatics, Micromagnetics, Mixed finite element method, Non-local constitutive modelling
in
Archive of Applied Mechanics
volume
89
issue
6
pages
1085 - 1102
publisher
Springer
external identifiers
  • scopus:85055986715
ISSN
0939-1533
DOI
10.1007/s00419-018-1482-7
language
English
LU publication?
yes
id
22fcff63-13c0-44ed-b1eb-59714f47ca8a
date added to LUP
2018-11-22 09:51:02
date last changed
2019-11-13 05:21:03
@article{22fcff63-13c0-44ed-b1eb-59714f47ca8a,
  abstract     = {<p>Microstructure evolution in magnetic materials is typically a non-local effect, in the sense that the behaviour at a material point depends on the magnetostatic energy stored within the demagnetisation field in the entire domain. To account for this, we propose a finite element framework in which the internal state variables parameterising the magnetic and crystallographic microstructure are treated as global fields, optimising a global potential. Contrary to conventional micromagnetics, however, the microscale is not spatially resolved and exchange energy terms are neglected in this approach. The influence of microstructure evolution is rather incorporated in an effective manner, which allows the computation of meso- and macroscale problems. This approach necessitates the development and implementation of novel mixed finite element formulations. It further requires the enforcement of inequality constraints at the global level. To handle the latter, we employ Fischer–Burmeister complementarity functions and introduce the associated Lagrange multipliers as additional nodal degrees-of-freedom. As a particular application of this general methodology, a recently established energy-relaxation-based model for magnetic shape memory behaviour is implemented and tested. Special cases—including ellipsoidal specimen geometries—are used to verify the magnetisation and field-induced strain responses obtained from finite element simulations by comparison to calculations based on the demagnetisation factor concept.</p>},
  author       = {Buckmann, Karsten and Kiefer, Björn and Bartel, Thorsten and Menzel, Andreas},
  issn         = {0939-1533},
  keyword      = {Magnetic shape memory alloys,Magnetostatics,Micromagnetics,Mixed finite element method,Non-local constitutive modelling},
  language     = {eng},
  number       = {6},
  pages        = {1085--1102},
  publisher    = {Springer},
  series       = {Archive of Applied Mechanics},
  title        = {Simulation of magnetised microstructure evolution based on a micromagnetics-inspired FE framework : application to magnetic shape memory behaviour},
  url          = {http://dx.doi.org/10.1007/s00419-018-1482-7},
  volume       = {89},
  year         = {2019},
}