Advanced

Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal plasticity modeling

Issa, Sally LU ; Wallin, Mathias LU ; Ristinmaa, Matti LU and Hallberg, Håkan LU (2018) In Computational Mechanics p.1-13
Abstract

Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that... (More)

Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the plastic deformation gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Crystal plasticity, Diagonally implicit Runge–Kutta, Implicit Euler, Numerical integration
in
Computational Mechanics
pages
13 pages
publisher
Springer
external identifiers
  • scopus:85046009635
ISSN
0178-7675
DOI
10.1007/s00466-018-1572-y
language
English
LU publication?
yes
id
918b2e25-92be-4119-8ef6-69f8f3589202
date added to LUP
2018-05-15 13:11:07
date last changed
2018-05-29 10:57:15
@article{918b2e25-92be-4119-8ef6-69f8f3589202,
  abstract     = {<p>Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the plastic deformation gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.</p>},
  author       = {Issa, Sally and Wallin, Mathias and Ristinmaa, Matti and Hallberg, Håkan},
  issn         = {0178-7675},
  keyword      = {Crystal plasticity,Diagonally implicit Runge–Kutta,Implicit Euler,Numerical integration},
  language     = {eng},
  month        = {03},
  pages        = {1--13},
  publisher    = {Springer},
  series       = {Computational Mechanics},
  title        = {Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal plasticity modeling},
  url          = {http://dx.doi.org/10.1007/s00466-018-1572-y},
  year         = {2018},
}