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Les mousses fragiles font aujourd'hui partie des nouveaux matériaux très performants dont le procédé de fabrication permet un contrôle précis de la microstructure finale. De nouveaux débouchés apparaissent dans des applications structurales (absorption de choc, allègement des structures) en raison de leur excellente tenue mécanique alliée à une grande légèreté. Dans les travaux réalisés dans le cadre de cette thèse, une mousse carbone à cellules ouvertes a été étudiée dans le but d'être utilisée pour assurer la protection des capots de protection d'emballages. Le comportement mécanique en compression a été caractérisé sous des sollicitations uniaxiales et multiaxiales. La surface de charge de la mousse ainsi que son évolution au cours du chargement ont été identifiés. Les principales propriétés mécaniques ont été évaluées et certaines d'entre elles ont été corrélées avec celles prédites par le modèle micro-mécanique de Gibson et Ashby développé pour les mousses fragiles. Grâce aux observations post-mortem sous microscope électronique à balayage et en micro-tomographie aux rayons X, les mécanismes de déformation et d'absorption d'énergie ont été également caractérisés. Pour modéliser le comportement multiaxial en compression de la mousse carbone, considérée comme un milieu continu homogène et isotrope, le modèle de Deshpande et Fleck (DF) a été adopté et adapté. Ce modèle a été implanté dans le code éléments finis LS-DYNA. Il a été identifié et validé sur l'ensemble des essais triaxiaux disponibles ainsi que sur des essais d'écrasement de mini-structure. Le comportement macroscopique global, obtenu à l'aide de simulations numériques, est prédit de manière satisfaisante. Il sera amélioré par la suite pour prendre en compte certains aspects non décrits actuellement. / Due to improvements in the manufacturing process that allow a better control of their microstructure, brittle foams are now part of the new efficient materials. New markets in the field of structural applications open up thanks to their excellent mechanical properties combined with light weight.In this study, a carbon foam with open cells has been studied in order to be used as shock absorber in packagings. Its compressive mechanical behavior has been characterized under various uniaxial and multiaxial loadings. The carbon foam yield surface and its evolution during loading have been identified. The main mechanical properties have been evaluated and some of them have been correlated with those predicted by the Gibson and Ashby micromechanical model. The mechanisms of deformation and the energy absorption have been studied using post-mortem observations by scanning electron microscopy (SEM) and X-Ray microtomography.The Deshpande and Fleck model (DF) has been adopted and slightly modified to model the compressive multiaxial behavior of the carbon foam. The latter is considered as an homogeneous continuum medium. The constitutive equations have been implemented in the finite element code LS-DYNA via a Umat routine. The model parameters have been identified and the model estimations validated on available triaxial tests as well as on crushing tests made on micro-structures. Numerical simulations are relevant on predicting the global macroscopic behavior. Nevertheless, the mechanical model needs to be improved to better account for some phenomena not currently described.

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<div>This body of work examines analytical and numerical models to simulate the response of structures in shock absorption applications. Specifically, the work examines the prediction of cushion curves of polymer foams, and a topological examination of a $\chi$ shape unit cell found in architected mechanical elastomeric metamaterials. The $\chi$ unit cell exhibits the same effective stress-strain relationship as a closed cell polymer foam. Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are used within the packaging industry to characterize a foam's impact performance. These curves are two-dimensional representations of the deceleration of an impacting mass versus static stress. The main drawback with cushion curves is that they are currently generated from an exhaustive set of experimental test data. This work examines modeling the shock response using a continuous rod approximation with a given impact velocity in order to generate cushion curves without the need of extensive testing. In examining the $\chi$ unit cell, this work focuses on the effects of topological changes on constitutive behavior and shock absorbing performance. Particular emphasis is placed on developing models to predict the onset of regions of quasi-zero-modulus (QZM), the length of the QZM region and the cushion curve produced by impacting the unit cell. The unit cell's topology is reduced to examining a characteristic angle, defining the internal geometry with the cell, and examining the effects of changing this angle.</div><div>However, the characteristic angle cannot be increased without tradeoffs; the cell's effective constitutive behavior evolves from long regions to shortened regions of quasi-zero modulus. Finally, this work shows that the basic $\chi$ unit cell can be tessellated to produce a nearly equivalent force deflection relationship in two directions. The analysis and results in this work can be viewed as new framework in analyzing programmable elastomeric metamaterials that exhibit this type of nonlinear behavior for shock absorption.</div>