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Analyse morphologique et homogénéisation numérique : application à la pâte de ciment

Abstract : Classical homogenization schemes, based on the solution to Eshelby's inhomogeneity problem, draw their popularity from the fact that they are both robust (even infinite contrast of the mechanical phases is allowed) and versatile (linear- as well as non-linear mechanical problems can be addressed), while the computations involved are very limited. Their flaw lies in the fact that they incorporate very little morphological information: problems such as the influence of the pore-size distribution, or the local orientation of anisotropic inclusions is out of their reach. Presently, only lengthy full-field calculations (FEM, BEM) can address such issues. The aim of this work is to devise new homogenization techniques, which are not as computationally involved as FEM or BEM calculations, while capturing more details of the microstructure than Eshelby-based techniques. Two methods are developed within the framework of the variational principle of Hashin and Shtrikman, which provides sound mathematical ground. The polarized inclusion method, on the one hand, aims to address composites with inclusions embedded in a homogeneous matrix. On the other hand, FFT-based homogenization techniques are known to alleviate the burden of a full-field calculation carried out with FEM or BEM. With the help of the Hashin and Shtrikman principle, new light is shed on these techniques, and a new, faster and more robust, FFT-based scheme is proposed. The cement industry would certainly benefit from such advanced homogenization schemes, since the macroscopic properties of cement pastes are known to heavily rely on the finest details (at sub-micron length-scales) of the porous network (within the C-S-H phase). Part of this work is devoted to the characterization of this network using two experimental techniques, namely small-angle X-ray scattering and tomography with soft X-ray microscopy. Attempts are made at quantifying the microstructure of C-S-H, in order to improve the estimates of its mechanical properties. A link between these two approaches is established. This attempt, perfectible, shows that popular models for C-S-H cannot account for these experimental data.
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Contributor : Sébastien Brisard <>
Submitted on : Saturday, August 27, 2011 - 10:45:24 AM
Last modification on : Friday, July 17, 2020 - 5:09:09 PM
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  • HAL Id : tel-00617356, version 1


Sébastien Brisard. Analyse morphologique et homogénéisation numérique : application à la pâte de ciment. Mécanique []. Université Paris-Est, 2011. Français. ⟨tel-00617356⟩



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