Galerkin-based mechanical integrators for finite elastodynamics formulated in principal stretches - pitfalls and remedies
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1515157
- author
- Mohr, Rouven ; Menzel, Andreas LU and Steinmann, Paul
- organization
- publishing date
- 2008
- 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
- 2016-04-01 13:52:07
- date last changed
- 2022-01-27 21:32:46
@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}}, doi = {{10.1016/j.cma.2008.05.011}}, volume = {{197}}, year = {{2008}}, }