Comptes Rendus
no. 7
Model reduction, data-based and advanced discretization in computational mechanics
Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics
[Conservation et dissipation d'énergie dans les solides tridimensionnels en grandes transformations avec des degrés de liberté rotationnels en dynamique non linéaire]
Abir Boujelben1 ; Adnan Ibrahimbegovic2
1 Sorbonne Universités, Université de technologie de Compiègne, Laboratoire Roberval de mécanique, Centre de recherches de Royallieu, CS 60319, 60200 Compiègne cedex, France
2 Sorbonne Universités, Université de technologie de Compiègne, Laboratoire Roberval de mécanique, Chair of Computational Mechanics, Centre de recherches de Royallieu, CS 60319, 60200 Compiègne cedex, France
Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 571-580.

Dans cet article, nous développons un schéma implicite d'intégration temporelle capable d'assurer, soit la conservation de l'énergie, soit la dissipation de l'énergie d'un système dynamique non linéaire. Ce dernier est particulièrement intéressant pour améliorer la stabilité numérique pour le calcul sur un grand intervalle du temps. L'implémentation de la méthode des éléments finis est présentée en détail pour un modèle de solide tridimensionnel en grandes transformations qui fait intervenir des degrés de liberté de rotation indépendants. La prise en compte de la rotation implique un choix judicieux de la mesure des grandes déformations pour séparer les grands déplacements des grandes rotations. La performance du schéma proposé est illustrée à travers de nombreux exemples de simulations.

In this work, we design a time-stepping scheme, which can ensure either conservation of energy or dissipation of energy of high (unresolved) modes for nonlinear dynamic analysis. The latter is needed to improve the performance in stress computation and long-term numerical stability. Finite element implementation details are given for finite-strain three-dimensional solid model with independent rotational degrees of freedom. The addition of a rotation field requires a particular choice of large strain measures, allowing one to separate large rotation and large displacement. Several numerical simulations illustrate a very satisfying performance of the proposed time-stepping scheme.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crme.2018.04.006
Keywords: 3D solids, Nonlinear dynamics, Large displacements and rotations, Conserving/decaying algorithms
Mot clés : Solide 3D, Dynamique non linéaire, Grandes transformations, Algorithme de conservation/dissipation
Abir Boujelben 1 ; Adnan Ibrahimbegovic 2

1 Sorbonne Universités, Université de technologie de Compiègne, Laboratoire Roberval de mécanique, Centre de recherches de Royallieu, CS 60319, 60200 Compiègne cedex, France
2 Sorbonne Universités, Université de technologie de Compiègne, Laboratoire Roberval de mécanique, Chair of Computational Mechanics, Centre de recherches de Royallieu, CS 60319, 60200 Compiègne cedex, France 
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     author = {Abir Boujelben and Adnan Ibrahimbegovic},
     title = {Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {571--580},
     publisher = {Elsevier},
     volume = {346},
     number = {7},
     year = {2018},
     doi = {10.1016/j.crme.2018.04.006},
     language = {en},
}
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Abir Boujelben; Adnan Ibrahimbegovic. Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics. Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 571-580. doi : 10.1016/j.crme.2018.04.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.006/

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