X-ray tomography is an imaging technique to inspect objects' internal structures with externally measured data by X-ray radiation non-destructively. However, there are concerns about X-ray radiation damage and tomographic acquisition speed in real-life applications. Strategies with insufficient measurements, such as measurements with insufficient dosage (low-dose) and measurements with insufficient projection angles (sparse-view), have been proposed to relieve these problems but are generally compromising imaging quality. Such a dilemma inspires the development of advanced tomographic imaging techniques, in particular, deep learning algorithms to improve reconstruction results with insufficient measurements. The overall aim of this thesis is to design efficient and robust data-driven algorithms with the help of prior knowledge from physics insights and measurement models. We first introduce a hierarchical synthesis CNN (HSCNN), which is a knowledge-incorporated data-driven tomographic reconstruction method for sparse-view and low-dose tomography with a split-and-synthesis approach. This proposed learning-based method informs the forward model biases based on data-driven learning but with reduced training data. The learning scheme is robust against sampling bias and aberrations introduced in the forward modeling. High-fidelity X-ray tomographic imaging reconstruction results are obtained with a very sparse number of projection angles for both numerical simulated and physics experiments. Comparison with both conventional non-learning-based algorithms and advanced learning-based approaches shows improved accuracy and reduced training data size. As a result of the split-and-synthesis strategy, the trained network could be transferable to new cases. We then present a deep learning-based enhancement method, HDrec (hybrid-dose reconstruction algorithm), for low-dose tomography reconstruction via a hybrid-dose acquisition strategy composed of textit{extremely sparse-view normal-dose measurements} and textit{full-view low-dose measurements}. The training is applied for each individual sample without the need of transferring the trained models for other samples. Evaluation of two experimental datasets under different hybrid-dose acquisition conditions shows significantly improved structural details and reduced noise levels compared to results with traditional analytical and regularization-based iterative reconstruction methods from uniform acquisitions under the same amount of total dosage. Our proposed approach is also more efficient in terms of single projection denoising and single image reconstruction. In addition, we provide a strategy to distribute dosage smartly with improved reconstruction quality. When the total dosage is limited, the strategy of combining a very few numbers of normal-dose projections and with not-too-low full-view low-dose measurements greatly outperforms the uniform distribution of the dosage throughout all projections. We finally apply the proposed data-driven X-ray tomographic imaging reconstruction techniques, HSCNN and HDrec, to the dynamic damage/defect characterization applications for the cellular materials and binder jetting additive manufacturing. These proposed algorithms improve data acquisition speeds to record internal dynamic structure changes. A quantitative comprehensive framework is proposed to study the dynamic internal behaviors of cellular structure, which contains four modules: (i) In-situ fast synchrotron X-ray tomography, which enables collection of 3D microstructure in a macroscopic volume; (ii) Automated 3D damage features detection to recognize damage behaviors in different scales; (iii) Quantitative 3D structural analysis of the cellular microstructure, by which key morphological descriptors of the structure are extracted and quantified; (iv) Automated multi-scale damage structure analysis, which provides a quantitative understanding of damage behaviors. In terms of binder jetting materials, we show a pathway toward the efficient acquisition of holistic defect information and robust morphological representation through the integration of (i) fast tomography algorithms, (ii) 3D morphological analysis, and (iii) machine learning-based big data analysis. The applications to two different 4D material characterization demonstrate the advantages of these proposed tomographic imaging techniques and provide quantitative insights into the global evolution of damage/defect beyond qualitative human observation. / Doctor of Philosophy / X-ray tomography is a nondestructive imaging technique to visualize interior structures of non-transparent objects, which has been widely applied to resolve implicit 3D structures, such as human organs and tissues for clinical diagnosis, contents of baggage for security check, internal defect evolution during additive manufacturing, observing fracturing accompanying mechanical tests, and etc. Multiple planar measurements with sufficient X-ray exposure time among different angles are desirable to reconstruct the unique high-quality 3D internal distribution. However, there are practical concerns about X-ray radiation damage to biology samples or long-time acquisition for dynamic experiments in real-life applications. Insufficient measurements by reducing the number of total measurements or the time for each measurement, are proposed to solve this problem but doing so usually leads to the sacrifice of the reconstruction quality. Computational algorithms are developed for tomographic imaging under these insufficient measurement conditions to obtain reconstructions with improved quality. Deep learning has been successfully applied to numerous areas, such as in recognizing speech, translating languages, detecting objects, and etc. It has also been applied to X-ray tomographic imaging to improve the reconstruction results by learning the features through thousands to millions of corrupted and ideal reconstruction pairs. The aim of this thesis to design efficient deep learning-based algorithms with the help of physical and measurement priors to reduce the number of training datasets. We propose two different deep learning-based tomographic imaging techniques to improve reconstruction results with reduced training data under different insufficient measurement conditions. One way is to incorporate prior knowledge of the physics models to reduce the required amount of ground truth data, from thousands to hundreds. The training data requirement is further simplified with another hybrid measurement strategy, which could be implemented on each individual sample with only several high-quality measurements. In the end, we apply these two proposed algorithms to different dynamic damage/defect behavior characterization applications. Our methods achieve improved reconstruction results with greatly enhanced experimental speeds, which become suitable for dynamic 3D recording. Final results demonstrate the advantages of the proposed tomographic imaging techniques and provide quantitative insights into the global dynamic evolution inside the material. This quantitative analysis also provides a much more comprehensive understanding than qualitative human observation.

Inkjet printing is a versatile manufacturing method with applications beyond its traditional application in graphics and text printing, particularly in structural and functional materials. This thesis aims to enhance the understanding of DOD inkjet printing processes by investigating the behaviour of solvent mixtures and nanoparticle suspensions to identify the key parameters affecting drop ejection, drying and stacking processes. Drop ejection and flight were investigated with two modes of inkjet printheads, using a range of fluids formulated from solvent mixtures and characterised by the dimensionless Z number. The printable range was found to be 1.17 smaller or equal to Z smaller or equal to 36.76 for a 10 pl (21.5 micro metre diameter) shear-mode Dimatix printhead. However, with an 80 micro metre diameter squeeze-mode MicroFab printhead, the range was found to be narrower with 4.02 smaller or equal to Z smaller or equal to 16.2. However, both printheads were found to show a printable range of Weber number with 0.4 <We <20. Weber number is determined by the drop velocity and hence the actuating pulse. When designing inks for future printing work, not only the fluid properties, but also the pulse voltages need to be considered. The drop stacking and solidification processes of drops containing nano ZrO2 particles were investigated to enhance the understanding of drop drying and drop/drop interactions. In-situ synchrotron X-ray radiography provides a promising method to track the time-evolved solid segregation within printed drops during drying. Both the initial contact angle and substrate temperature during printing strongly influence the drying process and the final dried deposit shape. The drops were first pinned and then there was a slight sliding of the three-phase contact line. Drops were deformed by the stacking of overprinted drops when printed on Kapton tapes and silicon wafer surfaces, but not on glass slides due to the small contact angle of water on glass slides. Crack-like defects were found at the edge of the final dried stacking structures. The coffee stain effects within a single inkjet printed droplet and the 3D structures before and after sintering were investigated to find out the influence of ink properties, printing parameters and substrate temperature on inkjet printed structures. It was found coffee staining was more obvious at high substrate temperatures. When adding 25 vol% ethylene glycol (EG) or 5 wt% polyethylene glycol (PEG), the coffee stain effect is reduced or eliminated under room temperature drying. X-ray tomography has been demonstrated as a valuable tool for the characterization of 3D printed objects and defects that form during their manufacture. Defects were characterised as microvoids or large-scale crack-like defects. The majority of the microvoids revealed are associated with mechanisms and processes within a single drop, e.g. segregation during dryings such as the formation of coffee stains or coffee rings. The size or distribution of microvoids can be controlled by changing the ink formulation, with higher PEG content inks showing lower concentrations of microvoids.

L’anatomie interne des crânes des stégocéphales Stanocephalosaurus (Temnospondyli), Laosuchus (Chroniosuchia) et Diplocaulus (Lepospondyli) a pu être révélée par l’utilisation de la tomographie à rayons X et a permis de mieux comprendre leur paléobiologie : 1) l’oreille moyenne de Stanocephalosaurus serait adaptée à la perception de sons dans le milieu subaquatique ; 2) des canaux sensoriels intra-osseux ont été identifiés chez Laosuchus. La morphologie endocrânienne a ensuite été utilisée dans une analyse phylogénétique portant sur les relations de parentés controversées entre stégocéphales et lissamphibiens. Cette analyse montre que la monophylie des lissamphibiens serait due à un phénomène d’attraction des longues branches, résultant de l’optimisation de la simplification crânienne, identifiée comme une convergence. Les morphologies de la boite crânienne, du stapes et du palais favorisent une origine diphylétique des lissamphibiens parmi les temnospondyles. / The intracranial anatomy of the stegocephals Stanocephalosaurus (Temnospondyli), Laosuchus (Chroniosuchia) and Diplocaulus (Lepospondyli) has been revealed by X-rays tomography and allowed to better understand their paleobiology: 1) the middle ear of Stanocephalosaurus would be an underwater adapted hearing system; 2) intraosseous sensorial canals have been identified in Laosuchus. The endocranial morphology have been included in a phylogenetic analysis on the debated relationships between stegocephals and lissamphibians. This analysis shows that the monophyly of Lissamphibia may result from a long-branch attraction, due to the optimisation of the cranial simplification, here as identified convergent. The morphologies of braincase, stapes and palate favour a biphyletic origin of lissamphibians among temnospondyls.

Ein Schwerpunkt der Arbeit ist die lokale Phasenanalyse keramischer Systeme mittels EBSD. Insbesondere bei MMC auf der Basis von TRIP-Stahl/Mg-PSZ ist die Ortsauflösung der bisher üblichen XRD-Phasenanalyse nicht ausreichend. Das gilt auch für die Analyse von Grenzflächenreaktionen, wie sie zum Beispiel bei Korrosionsprozessen auftreten. Es wurde eine Methode der Probenpräparation entwickelt und erfolgreich für unterschiedliche keramische Systeme eingesetzt. Ein Ergebnis ist der Nachweis von spannungs-assistierten Phasenumwandlungen in Mg-PSZ. Zweiter Schwerpunkt ist die Entwicklung einer in situ Druckverformungsapparatur für einen Labor-Röntgen-Tomographen. Mit dieser Apparatur können Druckverformungskräfte bis 100 kN erreicht werden. Tomographische Untersuchungen werden unter Druckspannung durchgeführt. Im Rahmen der Arbeit wurde insbesondere das Verformungs- und Schädigungsverhalten von MMC in Form von Schäumen und Wabenkörpern detailliert untersucht.

In this study, imaging with ionizing radiation was evaluated as a research technique in coal research. Part of the evaluation was to conduct a thorough literature survey as well as a preliminary investigation into coal pyrolysis and gasification with micro–focus X–ray tomography. The literature survey summarizes previous research experiences, primarily focussing on the possibility of utilizing a specific coal bed for carbon dioxide sequestration and methane production. This includes quantifying the fracture and cleat network and visualizing the orientation of this network. The cleat and fracture spacing and aperture are used to calculate certain parameters necessary to model gas flow. Other aspects include non–destructive characterization which consisted of determining the porosity and the minerals and macerals present and the respective mineral distribution. The literature survey also includes a section on the utilization of neutrons in coal research and a description of a neutron imaging facility in South Africa is presented. Three coal samples from the Waterberg and Highveld regions of South Africa were used to investigate the process of pyrolysis through micro–focus X–ray tomography. The samples swelled significantly when 50% pyrolysis was achieved after which the samples became brittle. This verified the plastic nature of the coal, that is prevalent under these conditions. It was also possible to perform qualitative characterizations prior to and during the process. Regions of low and high density materials could also be visualized. The distribution of the minerals is indicative of the permeability of the organic matrix. Two coal samples of the Highveld regions were used to investigate gasification up to a level of 30%. It was possible to verify that the reaction progressed according to the mechanisms proposed by the un–reacted shrinking core model. The mineral matter and the high density coal macerals did not influence the reaction in any way. / http://hdl.handle.net//10394/7008 / Thesis (M.Ing. (Chemical Engineering))--North-West University, Potchefstroom Campus, 2012.

In this study, imaging with ionizing radiation was evaluated as a research technique in coal research. Part of the evaluation was to conduct a thorough literature survey as well as a preliminary investigation into coal pyrolysis and gasification with micro–focus X–ray tomography. The literature survey summarizes previous research experiences, primarily focussing on the possibility of utilizing a specific coal bed for carbon dioxide sequestration and methane production. This includes quantifying the fracture and cleat network and visualizing the orientation of this network. The cleat and fracture spacing and aperture are used to calculate certain parameters necessary to model gas flow. Other aspects include non–destructive characterization which consisted of determining the porosity and the minerals and macerals present and the respective mineral distribution. The literature survey also includes a section on the utilization of neutrons in coal research and a description of a neutron imaging facility in South Africa is presented. Three coal samples from the Waterberg and Highveld regions of South Africa were used to investigate the process of pyrolysis through micro–focus X–ray tomography. The samples swelled significantly when 50% pyrolysis was achieved after which the samples became brittle. This verified the plastic nature of the coal, that is prevalent under these conditions. It was also possible to perform qualitative characterizations prior to and during the process. Regions of low and high density materials could also be visualized. The distribution of the minerals is indicative of the permeability of the organic matrix. Two coal samples of the Highveld regions were used to investigate gasification up to a level of 30%. It was possible to verify that the reaction progressed according to the mechanisms proposed by the un–reacted shrinking core model. The mineral matter and the high density coal macerals did not influence the reaction in any way. / http://hdl.handle.net//10394/7008 / Thesis (M.Ing. (Chemical Engineering))--North-West University, Potchefstroom Campus, 2012.

.La densification du névé en glace est un processus essentiel à comprendre pour interpréter les enregistrements climatiques. Une bonne connaissance des mécanismes permet une datation précise de l'air capturé dans la glace lors de la fermeture des pores. Celle-ci est plus vieille que l'air capturé à cause du transport des gaz dans la colonne de névé plus rapide que la densification de celui-ci. Cette différence d'âge entre la glace et le gaz est généralement appelé le Δage. La densification de la neige consiste en un processus complexe de réarrangement de grains, de frittage et de déformation viscoplastique. Bien que le comportement viscoplastique du cristal de glace soit fortement anisotrope, les modèles de densification actuels ne tiennent pas compte de cette anisotropie. De plus, le caractère granulaire du névé affecte aussi sa densification. La relation entre la fermeture des pores et les mécanismes microstructuraux sous-jacents est encore méconnue. Le but de cette thèse est d'incorporer l'aspect granulaire ainsi que l'anisotropie du cristal de glace dans une approche de modélisation innovante de la densification. Des expériences sur l'indentation viscoplastique de cylindres monocristallins de glace ont été réalisées pour proposer une loi de contact basée sur la théorie de l'indentation, et prenant en compte la déformation préférentielle du cristal de glace sur les plans basaux. Cette loi de contact a été implémentée dans un code utilisant la méthode des éléments discrets pour prédire la densification du névé.La micro-tomographie aux rayons X a été utilisée pour caractériser ex situ le névé polaire en trois dimensions à différentes étapes de la densification (ρ= 0.55-0.88 g/cm3), i.e. pour différentes profondeurs (~23 à 130m). Une étude fine de la fermeture des pores et de différentes caractéristiques morphologiques et physiques a été réalisée pour les sites polaires Dome C et Lock In. Des essais mécaniques ont aussi été réalisés in situ sur du névé extrait de Dome C dans le but de modéliser la densification du névé. Les observations microstructurales des expériences ex situ et in situ révèlent d'importantes différences dues aux vitesses relativement importantes utilisées lors des essais mécaniques. Ces vitesses rapides permettent de découpler la contribution des cinétiques de diffusion de la contribution viscoplastique de la déformation. Les effets de ces contributions sur la morphologie des pores et leurs fermetures sont discutés. Pour caractériser la fermeture des pores, cette thèse propose un indice de connectivité définit par le ratio entre le volume du plus gros pore sur la porosité totale. En effet, cet indice est plus approprié lors de l'utilisation de la tomographie aux rayons X que le ratio de pores fermés pour prédire la densité au close-off. / Densification from firn to ice is an essential phenomenon to understand for the interpretation of the climate record. A good knowledge of this mechanism enables the precise dating of the air embedded in the ice. The step at which the air becomes entrapped is the pore closure (or close-off). Because of gas flow in the firn column, the ice is older than the entrapped air. The difference between ice and gas is generally defined as Δage.Snow densification consists of grain rearrangements, sintering and viscoplastic deformation. Although the viscoplastic behaviour of the ice crystal is strongly anisotropic, densification models do not take into account this anisotropy. Firn also bears some granular characteristics that may affect its densification. The interactions between pore closure and microstructural mechanisms in the firn are still misunderstood.The aim of this PhD thesis is to incorporate both the granular aspect of firn and its anisotropy into an innovating approach of firn densification modelling. The mutual indentation of viscoplastic monocrystalline ice cylinders was experimentally carried out to propose a contact law that is based on indentation theory and that takes into account the preferential viscoplastic deformation on the basal plane. We have integrated this contact law into a DEM (Discrete Element Method) code for the prediction of firn densification.3D X-ray micro-tomography was performed on polar firn at different stages of the densification (ρ= 0.55-0.88 g/cm3) and depths (~23 to 130m). A thorough investigation of pore closure and of different morphological and physical parameters was achieved for the Dome C and the newly drilled Lock In polar sites. In addition to these ex situ analyses, in situ X-ray micro-mechanical experiments were carried out on firn extracted from Dome C in order to model its densification. Ex situ and in situ microstructural observations indicate significant differences that can be explained by the relatively large strain-rates imposed to the firn during in situ tests. These large strain rates allow for a decoupling of the effects of diffusion kinetics and of viscoplastic deformation. Their relative weights on the morphology of pores and on their closure are discussed. To measure pore closure, we propose a connectivity index, which is the ratio of the largest pore volume over the total pore volume. We show that this index is better suited for X-ray tomography analysis than the classic closed porosity ratio to predict the close-off density

abstract: Shock loading is a complex phenomenon that can lead to failure mechanisms such as strain localization, void nucleation and growth, and eventually spall fracture. The length scale of damage with respect to that of the surrounding microstructure has proven to be a key aspect in determining sites of failure initiation. Studying incipient stages of spall damage is of paramount importance to accurately determine initiation sites in the material microstructure where damage will nucleate and grow and to formulate continuum models that account for the variability of the damage process due to microstructural heterogeneity, which is the focus of this research. Shock loading experiments were conducted via flyer-plate impact tests for pressures of 2-6 GPa and strain rates of 105/s on copper polycrystals of varying thermomechanical processing conditions. Serial cross sectioning of recovered target disks was performed along with electron microscopy, electron backscattering diffraction (EBSD), focused ion beam (FIB) milling, and 3-D X-ray tomogrpahy (XRT) to gain 2-D and 3-D information on the spall plane and surrounding microstructure. Statistics on grain boundaries (GB) containing damage were obtained from 2-D data and GBs of misorientations 25° and 50° were found to have the highest probability to contain damage in as-received (AR), heat treated (HT), and fully recrystallized (FR) microstructures, while {111} Σ3 GBs were globally strong. The AR microstructure’s probability peak was the most pronounced indicating GB strength is the dominant factor for damage nucleation. 3-D XRT data was used to digitally render the spall planes of the AR, HT, and FR microstructures. From shape fitting the voids to ellipsoids, it was found that the AR microstructure contained greater than 55% intergranular damage, whereas the HT and FR microstructures contained predominantly transgranular and coalesced damage modes, respectively. 3-D reconstructions of large volume damage sites in shocked Cu multicrystals showed preference for damage nucleation at GBs between adjacent grains of a high Taylor factor mismatches as well as an angle between the shock direction and the GB physical normal of ~30°-45°. 3-D FIB sectioning of individual voids led to the discovery of uniform plastic zones ~25-50% the size of the void diameter and plastic deformation directions were characterized via local average misorientation maps. Incipient transgranular voids revealed from the sectioning process were present in grains of high Taylor factors along the shock direction, which is expected as materials with a low Taylor factor along the shock direction are susceptible to growth due their accomodation of plastic deformation. Fabrication of square waves using photolithography and chemical etching was developed to study the nature of plasticity at GBs away from the spall plane. Grains oriented close to <0 1 1> had half the residual amplitudes than grains oriented close to <0 0 1>. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2015

abstract: Aluminum alloys are ubiquitously used in almost all structural applications due to their high strength-to-weight ratio. Their superior mechanical performance can be attributed to complex dispersions of nanoscale intermetallic particles that precipitate out from the alloy’s solid solution and offer resistance to deformation. Although they have been extensively investigated in the last century, the traditional approaches employed in the past haven’t rendered an authoritative microstructural understanding in such materials. The effect of the precipitates’ inherent complex morphology and their three-dimensional (3D) spatial distribution on evolution and deformation behavior have often been precluded. In this study, for the first time, synchrotron-based hard X-ray nano-tomography has been implemented in Al-Cu alloys to measure growth kinetics of different nanoscale phases in 3D and reveal mechanistic insights behind some of the observed novel phase transformation reactions occurring at high temperatures. The experimental results were reconciled with coarsening models from the LSW theory to an unprecedented extent, thereby establishing a new paradigm for thermodynamic analysis of precipitate assemblies. By using a unique correlative approach, a non-destructive means of estimating precipitation-strengthening in such alloys has been introduced. Limitations of using existing mechanical strengthening models in such alloys have been discussed and a means to quantify individual contributions from different strengthening mechanisms has been established. The current rapid pace of technological progress necessitates the demand for more resilient and high-performance alloys. To achieve this, a thorough understanding of the relationships between material properties and its structure is indispensable. To establish this correlation and achieve desired properties from structural alloys, microstructural response to mechanical stimuli needs to be understood in three-dimensions (3D). To that effect, in situ tests were conducted at the synchrotron (Advanced Photon Source) using Transmission X-Ray Microscopy as well as in a scanning electron microscope (SEM) to study real-time damage evolution in such alloys. Findings of precipitate size-dependent transition in deformation behavior from these tests have inspired a novel resilient aluminum alloy design. / Dissertation/Thesis / Doctoral Dissertation Materials Science and Engineering 2017

Les matériaux polymères à structures cellulaires allient des propriétés mécaniques, thermiques, chimiques et optiques intéressantes aux regards des contraintes d’allègement des systèmes et des structures. Toutefois, pour diversifier leurs applications et les rendre toujours plus performants dans les domaines de la santé, du transport ou encore du bâtiment, une étude fine des relations qui lient les procédés de fabrication à la microstructure générée et aux propriétés qui en découlent, doit être menée. Ces propriétés mécaniques dépendent étroitement des propriétés de la matière dont les mousses sont faites mais aussi de la morphologie de leurs microstructures (orientation, distribution et taille des pores, épaisseur des parois). Il est donc crucial de pouvoir quantifier et mesurer ces paramètres pour tendre vers une compréhension fine des propriétés mécaniques et définir des modèles capables de relier le comportement macroscopique du matériau cellulaire vis-à-vis de son « équivalent » massif et de la microstructure. En collaboration étroite avec la direction recherche et développement de l’entreprise INTEREP, leader européen du caoutchouc cellulaire étanche, une caractérisation expérimentale du comportement mécanique de mousses de différentes natures polymériques et de différentes topologies à d’abord été effectuée. Ensuite un ensemble de modélisations géométriques a été développé à partir d’observations microstructurales de vraies mousses en micro-tomographie RX et à partir de microstructures générées virtuellement par le biais d’une description physique du processus de fabrication de mousses polymères. Finalement, une simulation numérique éléments finis en 2D et en 3D de ces microstructures couplées à la caractérisation expérimentale du matériau massif des parois a permis de reproduire et d’étudier finement les mécanismes de déformations observés expérimentalement sur des mousses polymères et d’affiner les lois de comportement empiriques avec la prise en compte d’un paramètre supplémentaire caractéristique de la statistique de distribution des cellules dans l’espace, c'est-à-dire de leurs localisations et de leur distribution de taille et de forme. / Polymer foams materials combine mechanical, thermal, chemical and optical interesting properties going with light weighting structures problems. However, to diversify their applications and make them even more efficient in health field, transportation or building, a fine study of the relationships between manufacturing processes to generated microstructures and resulting properties must be conducted. These mechanical properties are highly depending on the properties of material with which foams are made but also on the morphology of their microstructures (orientation, distribution and pore size, wall thickness). Thus it is crucial to quantify and measure these parameters to strive for a detailed understanding of the mechanical properties and define models capable of linking global behavior of cellular materials to bulk materials and microstructures. Working closely with research and development division of INTEREP, European leader in waterproof cellular rubber, an experimental characterization of the mechanical behavior of polymer foams of different natures and different topologies has been performed first. Then geometrical modeling was developed from micro structural observations of real foams in x-ray micro-tomography and from virtually generated microstructures through a physical description of polymer foams manufacturing process. Finally finite element simulation in 2D and 3D of these microstructures were coupled with the experimental characterization of bulk material allowing thus to reproduce and finely study deformation mechanisms experimentally observed on polymer foams and refine empirical behavior laws by taking into account additional characteristic parameter of cells statistical distribution in space like their location and their size distribution and shape.