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Imagerie 3D et simulation numérique pour l'étude multi-échelles de la compression d'une poudre constituée de grains déformables

Abstract : The work achieved in this thesis aims to study the mechanical behaviour of a powder made of deformable grains using, in a complementary way, experimental tests and numerical methods. For that purpose, a polymeric powder is mechanically tested inside a micro-tomograph. Such an apparatus allows for acquiring 3D images in order to ascertain and analyse the evolution of the micro-structure during loading. The 3D image analysis is associated to the Multi-Particles Finite Element Method (MP-FEM) in order to obtain a numerical model of the granular medium. This method simulates the mechanical behaviour of a set of grains deforming according to an elastic-plastic constitutive law and interacting through contact. A comprehensive method was developed with the aim of allowing such a multi-scale analysis. The simulated mechanical response of the granular material is comparable to the experimental response.Polystyrene was chosen to be the constituent of the granular medium for which the grains morphology is relatively heterogeneous. The powder is mechanically characterised using triaxial compression tests, performed at various confining pressures. The loading device is inserted into an X-ray tomograph in order to observe the evolution of the granular micro-structure inside the sample at various loading steps. A numerical code is used to perform Digital Volume Correlation (DVC) on the volumes from the tomography to determine a displacement field, and then, a strain field. The density analysis is also made possible thanks to X-ray tomography. Aiming at the study of the granular medium during loading, the observed particles on the 3D images from tomography are individually identified, meshed and added into a multi-particles finite element model. The boundary conditions imposed to the numerical sample are generated by imposing to the grains located at the border of the sample, displacements of the same amplitude and the same direction than the displacements known from DVC at the same locations.The finite element simulations are carried out on subvolumes of the real experimental sample made of a hundred to several hundreds of grains. The mean deformation of the numerical sample is calculated and directly compared with the measured deformation from DVC on the corresponding subvolume. This comparison shows that the method to generate the boundary conditions in the mechanical simulation is correct. It is observed, nevertheless, that the study of the local densification of the powder at the high strains is dependent on the size of the simulated volume. The averaged stress tensor inside the simulated volume is also calculated in order to determine the stress state in the subvolume of the sample depending on the chosen constitutive material of the grains. Several simulations, performed at various subvolumes, make the generation of a stress field possible. Taking into consideration the number of calculations needed to achieve this task, only the evolution of the stress on the median axis of the sample was estimated in this work. Computing the axial stress with simulations has another benefit: the choice of some mechanical properties of the constitutive material of the grains in the simulation enables to reach the axial stress measured on the real sample, and thus, to characterise the mechanical properties of the grains in interaction.
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https://hal.archives-ouvertes.fr/tel-02910925
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Submitted on : Monday, August 3, 2020 - 12:33:38 PM
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Maxime Teil. Imagerie 3D et simulation numérique pour l'étude multi-échelles de la compression d'une poudre constituée de grains déformables. Mécanique des solides [physics.class-ph]. Université Grenoble Alpes, 2019. Français. ⟨NNT : 2019GREAI086⟩. ⟨tel-02910925⟩

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