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Prédiction fiable de l'endommagement ductile par la méthode des éléments finis mixtes : endommagement non local et adaptation de maillage

Abstract : The aim of this thesis is to develop an accurate numerical model to predict damage growth and failure in ductile solids. These developments are done within a parallel finite element library called CIMLib. To deal with the incompressibility of plastic deformations, a mixed velocity-pressure finite element approximation with a stabilized discretization P1+/P1 is used to solve mechanical equations. The numerical analysis of an elastic-plastic damage law in this approximation has been widely discussed. An enhanced Lemaitre damage evolution law is considered. Coupled dissipative phenomena, influence of stress triaxiality ratio, and crack-closure effects under compressive conditions are taken into account in this formulation. A nonlocal damage approach, based on an implicit gradient formulation, is used. This nonlocal approach enables to avoid the localization phenomenon and the associated mesh dependency. The well-known physical plastic strain localization in shear bands is modelled to prove that the proposed approach gives reliable and physical results. An another main focus of this thesis is the anisotropic mesh adaptation to the damage phenomenon. An anisotropic adaptive meshing scheme has been applied to increase the accuracy of the damage variable with minimum computing time. Moreover the numerical tests have proven that this mesh adaptation strategy allows our approach to predict accurately the expected damaged and fractured areas. The last contribution of this work is the implementation of a geometric multigrid preconditioner in order to allow an efficient computation for large linear systems from a FE approximation. The first validations have shown a quasi-linear growth of the cpu-time as a function of the number of degrees of freedom. The developed numerical model can be used to simulate sheet metal joining processes based on material plastic deformation and to study their mechanical strength. In the future, these developments will also useful for other cold metal forming processes, such as forging, stamping, cutting ...
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Submitted on : Thursday, February 17, 2011 - 10:29:38 AM
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  • HAL Id : pastel-00566805, version 1

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Rachid El Khaoulani. Prédiction fiable de l'endommagement ductile par la méthode des éléments finis mixtes : endommagement non local et adaptation de maillage. Mécanique des matériaux [physics.class-ph]. École Nationale Supérieure des Mines de Paris, 2010. Français. ⟨NNT : 2010ENMP0001⟩. ⟨pastel-00566805⟩

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