Modélisation des propriétés mécaniques anisotropes aléatoires et impacts sur la propagation des ondes élastiques

Abstract : The aim of this thesis is to take into account the heterogeneity, the anisotropy and the uncertainties within 3D numerical simulation of elastic waves propagation. Firstly, the elasticity tensor field is modeled by means of a stochastic tensor-valued field. Its construction is generalized from the model of Soize [2008]. Hence, our model preserves principle properties of the former : a small set of parameters controlling the whole dispersion and the characteristic size of spatial variability, a local behavior being a priori arbitrary anisotropic (triclinic anisotropy) andothers essential mathematical properties. Moreover, a new parameter is added in order to impose a desired anisotropy mean level. Secondly, we carry out adaptations of an existing spectral finite elements-based elastic waves simulation software, namely the SPEC3D parallel computing code. On the one hand a sample generator of the elasticity random field model is implemented and on the other hand anisotropic material behavior is introduced in the elastodynamic solver. Finally, numerical parametric studies are performed using SPEC3D highlighting influences of heterogeneity and anisotropy on elastic waves behavior. In particular, it is observed that the characteristic time beyond which a multiple scattering pattern can be approximated by a diffusion regime directly depends on the correlation length of elasticity tensor field model. This time is detected by an energy equipartition between rotational and irrotational movements.
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Autre. Ecole Centrale Paris, 2011. Français. 〈NNT : 2011ECAP0006〉
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Submitted on : Wednesday, April 27, 2011 - 12:19:17 PM
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Quang Anh Ta. Modélisation des propriétés mécaniques anisotropes aléatoires et impacts sur la propagation des ondes élastiques. Autre. Ecole Centrale Paris, 2011. Français. 〈NNT : 2011ECAP0006〉. 〈tel-00589052〉



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