Homogénéisation en viscoélasticité linéaire non-vieillissante par la méthode de l'inclusion équivalente : application aux matériaux cimentaires

Abstract : The prediction of long-term behaviour of cementitious materials is a major concern which contributs to the study of the durability of prestressed structures. This work focuses on the use of the equivalent inclusion method, simplified multi-scale homogenization approach, for the prediction of creep in these materials. Creep is modelled by the non-ageing linear viscoelasticity. The equivalent inclusion method overcomes certain difficulties and limitations posed by conventional approaches. For cementitious materials (highly heterogeneous), conventional multi-scale approaches are, either digitally heavy and complex to implement, or not sufficiently detailed to take into account the specificities of a microstructure. The equivalent inclusion method presents a middle way and allows the calculation of simplified matrix-inclusion type microstructures and to provide estimates or bounds on the homogenized behaviour.Under its variational form, the equivalent inclusion method has, up to now, been implemented only for spherical inclusions. This work proposes to extend this method to ellipsoidal inclusions whose variation of slenderness allows the modelling of new aspheric elements such as cracks, fibers and portlandite crystals. Such enrichment of the geometry has an impact on the computation time, that is amplified in the context of creep. The second aspect of the work then applies to the extension of the equivalent inclusion method to the non-ageing linear viscoelasticity by means of the Laplace-Carson transform. An effective methodology (both from the viewpoint of precision and calculation time) is finally proposed to perform the numerical inversion of this transform
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Yassine El Assami. Homogénéisation en viscoélasticité linéaire non-vieillissante par la méthode de l'inclusion équivalente : application aux matériaux cimentaires. Génie civil. Université Paris-Est, 2015. Français. ⟨NNT : 2015PESC1051⟩. ⟨tel-01235752⟩

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