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Stratégies de couplage de modèles discret-continu en dynamique explicite

Abstract : Discrete models are widely used for describing brittle structures behavior, thanks to their ability to describe cracks propagation. Nonetheless, to provide realistic response such approaches required simulations at very small scales. To reduce the computational cost, an alternative is to identify regions where the use of discrete models is required, and a standard finite element model is used for the remaining regions. A decomposition of the domain is then introduced into two overlapping subdomains (one for each model). The coupling strategy is mainly based on the introduction on the overlapping region of each subdomain and of two ingredients : (i) a partition of unity of the energy (ii) Lagrange multipliers to enforce compatibility between subdomains. Then we analyze for such multimodel approaches the use of Lagrange multipliers at the boundary of the overlapping region instead of the complete overlapping region. The main advantage of such a coupling is the reduction of the size of the interface problem to be solved and the reduction of the computational cost for the same level of error. The properties of such a strategy are analyzed in both one and two dimensional dynamic problems and comparisons are provided. Following this work, multiscale aspect is extended to the time component. Indeed, it is not necessary to use the same time step in each subdomain provided by the stability condition of the Newmark scheme. About that, a subcycling strategy is applied. It consists to use a different time step in each subdomain. The key point is to elaborate a consistant approach based on the decrease of the dissipation. For that, a new predictor on interface quantities is designed to ensure continuity in the subcycling stage. Studies are raised on a one degree of freedom problem to illustrate the approach.
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https://tel.archives-ouvertes.fr/tel-00442682
Contributor : Ens Cachan Bibliothèque <>
Submitted on : Tuesday, December 22, 2009 - 11:42:19 AM
Last modification on : Thursday, December 10, 2020 - 10:53:05 AM
Long-term archiving on: : Thursday, June 17, 2010 - 10:07:14 PM

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  • HAL Id : tel-00442682, version 1

Citation

Sylvain Gavoille. Stratégies de couplage de modèles discret-continu en dynamique explicite. Mécanique [physics.med-ph]. École normale supérieure de Cachan - ENS Cachan, 2009. Français. ⟨tel-00442682⟩

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