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Développement d'une formulation arbitrairement lagrangienne eulérienne pour la simulation tridimensionnelle du laminage de produits plats

Abstract : Predicting profile and flatness defects of flat rolled products is a major concern of the current studies on rolling. It requires a three-dimensional model taking into account the deformation of cylinders leading to these defects. The mesh management of such a model is however difficult. The plastically strained area, necessary finely meshed, is generally very small compared to the total meshed volume. An appropriate mesh description is the Arbitrary Lagrangian Eulerian (ALE) formulation. The mesh is updated independently from the material motion. Thus, the ALE formulation allows to preserve mesh quality under severe deformations better than the lagrangian one and a refined strained area by being coupled with an adaptive mesh. In a previous work, a splitting ALE approach has been implemented in Forge3®. At each time step, the material velocity field is first computed (purely lagrangian stage), then the mesh velocity field is determined with the aim to optimize mesh quality without modifying connectivities (r-adaptation), and finally variables are remapped. A critical issue of the ALE method is to respect the geometry of the evolving free surfaces, particularly for processes with dominant tangential material motion, like rolling. For such cases, a new surface mesh management has been developed and used for the strip. It consists in projecting the surface nodes onto the intermediate surface computed at the end of the lagrangian stage. A smoothing surface method gives a higher degree of accuracy to the description of curved and coarsely meshed surfaces, for instance the crown appearing during rolling. All these procedures, a priori applicable to various geometries, are carried out locally for questions of efficiency and ease of implementation. This local characteristic does not restrain the choice of the time step thanks to a sub-stepping method. The elastic deformation of the cylinders is dealt with a quasi-eulerian formulation, which results in much smaller mesh sizes compared to a lagrangian one. An industrial rolling case was modelled with the ALE formulation. The computational times are significantly reduced compared to the lagrangian formulation of Forge3®. The results regarding efforts, stresses, etc. are generally better in ALE than in lagrangian and close to those of the quasi-eulerian formulation of Lam3.
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Submitted on : Tuesday, November 10, 2009 - 4:01:43 PM
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  • HAL Id : tel-00431051, version 1

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Sabine Philippe. Développement d'une formulation arbitrairement lagrangienne eulérienne pour la simulation tridimensionnelle du laminage de produits plats. Mécanique [physics.med-ph]. École Nationale Supérieure des Mines de Paris, 2009. Français. ⟨NNT : 2009ENMP1649⟩. ⟨tel-00431051⟩

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