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Modélisations multi-matériaux multi-vitesses en dynamique rapide

Abstract : Many simulations in fluid structure interactions, multiphase flows or dynamic impacts involve independent structures interacting through complex interfaces. For such problems, standard strategies often use a Lagrangian approach using one finite element mesh per structure and adequate matching strategies. These are very demanding in mesh generation, and are difficult to use in presence of large mesh distortions. An alternative is to use an Eulerian strategy describing the different structures on a single grid using a single average velocity field and developing ad hoc constitutive laws to handle the multiphase microstructure of each element. These models are usually quite crude on the interface physics. In this context, there is a renewed interest in models which will use a single global smooth mesh, not matching the structures and independent finite element velocity fields to describe the motion of the structures. This strategy is attractive but faces difficult challenges: interface tracking, development of adequate ALE formulations because materials and mesh velocities are different, proper treatment of the kinematic continuity constraints between the structures. Great care must be taken at this level in order to propose a stable approach which is locking free and stays robust in large strain elastodynamics. With this thesis, we propose an original strategy based on an enriched finite element method. It defines one FE velocity field by material on a single mesh, the different fields are overlapping and form an enriched field that can have a discontinuity at the interface and allows to describe sliding between the materials. The discontinuity is controlled by a normal velocity constraint at the interface and an additional unknown of interface pressure that is the Lagrange multiplier associated with the constraint. The ALE formulation used is based on a time split between Lagrangian phase and remap phase. The Lagrangian phase is solved by the Wilkins explicit scheme widely used while the remap is done by mesh intersections between Lagrangian meshes deformed by material and a smoothed average mesh. The interface is tracked during the remap by the volume fraction of each material in the cells and it reconstruction can be discontinuous across elements. Two variants of the methods are introduced, analysed and compared. They differ by their Lagrange multiplier discretization and consequently by their velocity constraint discretization: -the node continuity uses a Lagrange multiplier defined at nodes. This variant is simple and fast but does not take correctly into account the compressibility of materials, -the cell continuity uses a Lagrange multiplier constant by interface segment. This variant gives better results than the first one. The method is stabilized by adding internal nodes in the mixed cells using piecewise linear velocity shape functions inside each element and a proper mass lumping ensures a stable equilibration of the interface. The internal node momentum equation is discretized by an implicit scheme. The consequence is that a system coupling the interface nodes has to be solved in order to compute the velocities near the interface. The two variants have been implemented into an industrial code. They are validated and compared with several test cases involving different situations like fluid-structure interaction or sliding between solids.
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https://pastel.archives-ouvertes.fr/pastel-00803315
Contributor : Gauthier Folzan <>
Submitted on : Thursday, March 21, 2013 - 4:14:16 PM
Last modification on : Thursday, December 19, 2019 - 2:12:40 AM
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  • HAL Id : pastel-00803315, version 1

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Gauthier Folzan. Modélisations multi-matériaux multi-vitesses en dynamique rapide. Mécanique des solides [physics.class-ph]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00803315⟩

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