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Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response

Kiefer, Björn; Bartel, Thorsten and Menzel, Andreas LU (2012) In Smart Materials and Structures 21(9).
Abstract
Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic... (More)
Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Smart Materials and Structures
volume
21
issue
9
publisher
IOP Publishing
external identifiers
  • wos:000308867900008
  • scopus:84866118851
ISSN
0964-1726
DOI
10.1088/0964-1726/21/9/094007
language
English
LU publication?
yes
id
17327340-230e-4fe7-beac-ef993c69f2cc (old id 3167870)
date added to LUP
2012-11-15 18:08:54
date last changed
2017-08-27 03:39:24
@article{17327340-230e-4fe7-beac-ef993c69f2cc,
  abstract     = {Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases.},
  articleno    = {094007},
  author       = {Kiefer, Björn and Bartel, Thorsten and Menzel, Andreas},
  issn         = {0964-1726},
  language     = {eng},
  number       = {9},
  publisher    = {IOP Publishing},
  series       = {Smart Materials and Structures},
  title        = {Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response},
  url          = {http://dx.doi.org/10.1088/0964-1726/21/9/094007},
  volume       = {21},
  year         = {2012},
}