Homogénéisation périodique d’un matériau cellulaire en élasto-plasticité et application au calcul de structures : des petites aux grandes déformations

Abstract : Cellular materials have excellent specific properties, which make them attractive for aeronautical applications. However, modelling macroscopic structures including a cellular material is either very costly in terms of computational time if the whole mesoscopic structure is considered or a Homogeneous Equivalent Medium (HEM) has to be used. This Ph.D. dissertation presents, the characterisation of a cellular material built from a stacking of tubes with a square or hexagonal based pattern and the identification of a phenomenological model of their inelastic mechanical behaviour. First, the material is characterised for multi-axial loadings through a periodic finite element model in small deformations for each tube stacking pattern. The macroscopic behaviour is then used to identify a compressible anisotropic Homogeneous Equivalent Law (HEL). Within the infinitesimal strain hypothesis, a comparison is carried out between reference full scale models and HEM based ones of sandwich structures with a cellular core, confirming the relevance of the proposed multi-scale method. Then, the mechanical behaviour of each tube stacking is characterised for large deformations in order to study the influence of the boundary size effects and the instabilities in the core on the macroscopic behaviour of sandwich structures. After a study on the representative volume element, the macroscopic inelastic behaviour is characterised through the periodic homogenisation technique, especially the softening observed in compression for the hexagonal pattern. Finally, an extension of the HELs identified in small deformations is proposed to model the behaviour observed in large deformations.
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Alexandre Iltchev. Homogénéisation périodique d’un matériau cellulaire en élasto-plasticité et application au calcul de structures : des petites aux grandes déformations. Matériaux et structures en mécanique [physics.class-ph]. Ecole Nationale Supérieure des Mines de Paris, 2014. Français. ⟨NNT : 2014ENMP0044⟩. ⟨tel-01142233⟩

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