Méthode asymptotique numérique pour l'étude multi échelle des instabilités dans les matériaux hétérogènes

Abstract : The multiscale modelling of the heterogeneous materials is a challenge in computational mechanics. In the nonlinear case, the effective properties of heterogeneous materials cannot be obtained by the techniques used for linear media because the superposition principle is no longer valid. Hence, in the context of the finite element method, an alternative to mesh the whole structure, including all heterogeneities, is the use of the multiscale finite element method (FE2). These techniques have many advantages, such as taking into account : large deformations at the micro and macro scales, the nonlinear constitutive behaviors of the material, and microstructure evolution. The nonlinear problems in micro and macro scales are often solved by the classical Newton-Raphson procedures, which are generally suitable for solving nonlinear problems but have difficulties in the presence of instabilities. In this thesis, the combination of the multiscale finite element method (FE2) and the asymptotic numerical method (ANM), called Multiscale-ANM, allows one to obtain a numerical effective technique for dealing with the instability problems in the context of heterogeneous materials. These instabilities can occur at both micro and macro levels. Different classes of material constitutive relation have been implemented within our procedure. To improve the multiscale problem conditioning, a second order homogenization technique was also adapted in the framework of Multiscale-ANM technique. Furthermore, to reduce the computational time, some techniques been proposed in this work
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Saeid Nezamabadi. Méthode asymptotique numérique pour l'étude multi échelle des instabilités dans les matériaux hétérogènes. Autre. Université Paul Verlaine - Metz, 2009. Français. ⟨NNT : 2009METZ046S⟩. ⟨tel-01752669⟩

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