Quelques techniques pour appliquer la M.A.N. [Méthode Asymptotique Numérique] aux structures plastiques et aux grands systèmes

Abstract : Two studies have been carried out in the framework of the Asymptotic Numerical Method (A.N.M.). The first one deals with a new way to apply the reduced basis technique ton non linear elastic problems. This technique is usually applied to the non linear problem but here it is applied to the linear problems obtained by perturbation technique. Then, the computation of a considerable number of coefficients is avoid. Some examples have shown that it is possible to reduce the computation time, compared with the classical A.N.M. The second study deals with the application of the A.N.M. to elastoplastic problems in finite strains. Two formulations have been presented: - the first one is based on F. Sidoroff's model. This model allows one to work with small elastic strains but large plastic strains. The variational formulation is written with an updated lagrangian scheme. - The second formulation is based on J.C. Simo's model. The hyperelastic model used here allows one to work both with large elastic strains and large plastic strains. A Hu-Washizu mixed formulation is used, this leads to a three fields variational formulation. The elastoplastic models considered imply finite strain, non linear laws such as power laws and non regular relations. Some well established techniques have been carried out to compute power series in this framework. We have presented two different techniques for the regularisation of the flow rule, the first one leads to a type of deformation theory at each step and the second one introduces a viscoplastic regulation
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Ali Imazatene. Quelques techniques pour appliquer la M.A.N. [Méthode Asymptotique Numérique] aux structures plastiques et aux grands systèmes. Autre. Université Paul Verlaine - Metz, 2001. Français. ⟨NNT : 2001METZ008S⟩. ⟨tel-01748970⟩

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