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Galerkin-based mechanical integrators for finite elastodynamics formulated in principal stretches - pitfalls and remedies

Mohr, Rouven; Menzel, Andreas LU and Steinmann, Paul (2008) In Computer Methods in Applied Mechanics and Engineering 197(49-50). p.4444-4466
Abstract
In the present paper we deal with integrators relying on Finite Elements in time for general hyperelastic models which guarantee the conservation of the momentum maps as well as of the total energy within the calculation accuracy. In the isotropic case, eigenvalue-based constitutive laws are, on the one hand, very significant to model the behaviour of various materials. On the other hand, it will be shown that the efficient algorithmic treatment of principal stretches based on a perturbation approach requires, especially within the context of conserving schemes, advanced techniques to circumvent numerical problems. Accordingly, we propose an adequate solution strategy to avoid potential pitfalls which are related to numerical artefacts of... (More)
In the present paper we deal with integrators relying on Finite Elements in time for general hyperelastic models which guarantee the conservation of the momentum maps as well as of the total energy within the calculation accuracy. In the isotropic case, eigenvalue-based constitutive laws are, on the one hand, very significant to model the behaviour of various materials. On the other hand, it will be shown that the efficient algorithmic treatment of principal stretches based on a perturbation approach requires, especially within the context of conserving schemes, advanced techniques to circumvent numerical problems. Accordingly, we propose an adequate solution strategy to avoid potential pitfalls which are related to numerical artefacts of the applied non-standard quadrature rule. Finally, the excellent numerical and mechanical performance of the resulting Galerkin-based time-stepping schemes will be demonstrated by means of representative numerical examples. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Computer Methods in Applied Mechanics and Engineering
volume
197
issue
49-50
pages
4444 - 4466
publisher
Elsevier
external identifiers
  • wos:000260764700030
  • scopus:52749087634
ISSN
0045-7825
DOI
10.1016/j.cma.2008.05.011
language
English
LU publication?
yes
id
66704b5b-73e8-466a-99c2-aa8b7bce3838 (old id 1515157)
date added to LUP
2009-12-10 10:36:48
date last changed
2017-01-01 05:55:28
@article{66704b5b-73e8-466a-99c2-aa8b7bce3838,
  abstract     = {In the present paper we deal with integrators relying on Finite Elements in time for general hyperelastic models which guarantee the conservation of the momentum maps as well as of the total energy within the calculation accuracy. In the isotropic case, eigenvalue-based constitutive laws are, on the one hand, very significant to model the behaviour of various materials. On the other hand, it will be shown that the efficient algorithmic treatment of principal stretches based on a perturbation approach requires, especially within the context of conserving schemes, advanced techniques to circumvent numerical problems. Accordingly, we propose an adequate solution strategy to avoid potential pitfalls which are related to numerical artefacts of the applied non-standard quadrature rule. Finally, the excellent numerical and mechanical performance of the resulting Galerkin-based time-stepping schemes will be demonstrated by means of representative numerical examples.},
  author       = {Mohr, Rouven and Menzel, Andreas and Steinmann, Paul},
  issn         = {0045-7825},
  language     = {eng},
  number       = {49-50},
  pages        = {4444--4466},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {Galerkin-based mechanical integrators for finite elastodynamics formulated in principal stretches - pitfalls and remedies},
  url          = {http://dx.doi.org/10.1016/j.cma.2008.05.011},
  volume       = {197},
  year         = {2008},
}