Aluminum hexagonal honeycombs loaded in their tubular direction have extremely good mechanical properties, including high stiffness to weight and energy absorption capacities. The corresponding load-displacement curve exhibits a long plateau accompanied by small fluctuations. These fluctuations are due to the propagation of a folding front through the studied sample, which is due to the creation of folds. This plateau load makes honeycombs the perfect candidates for use as energy-dissipative devices such as bumpers. Previous studies have largely focused on the study of the plateau load with less attention given to the length of the folds. However, it will be seen that this parameter is crucial for both the complete understanding of the mechanics of the folding and the derivation of the plateau load. We present first an introduction to the thematic of honeycomb. Then, the first model focuses precisely on the fold length. Two hypotheses are considered, a correlation between elastic buckling and folding first and a local propagation of the existing fold secondly. The second hypothesis is found to be correct, and the results are good for thin foils. For thick foils, a geometric limitation occurs, which makes the results less precise. Then, we are able to use the previous kinematics for the folding and derive a new set of formulas for the plateau load. The results are compared with experimental results and past formulas, and are found to be good, especially for thin foils, where our results for the fold length are more precise.

This paper applies to the design and simulation of a shipping container made of sandwich panels. The amount of stresses acting on the body of the container is calculated and is optimized to reduce stresses for the better design output of the structure. The design aims to produce an application to reduce the tare weight of the container in order to increase the payload. Finite Element Analysis (FEA) is performed to evaluate the strength of structures of both old and new models helps us to compare which model is better and more efficient. Complete design and analysis is performed using Autodesk Inventor. / no

L'objectif de cette thèse est de développer des modèles d'homogénéisation analytiques de panneaux sandwichs en nid d'abeilles. A la différence des méthodes classiques, l'effet des peaux est pris en compte, conduisant à des propriétés mécaniques très différentes. Dans les cas des tractions, flexions, cisaillement dans le plan, cisaillements transversaux et torsion, différentes séries de fonctions analytiques sont proposées pour prendre en compte la redistribution des contraintes entre les parois du nid d'abeilles. Nous avons étudié l'influence de la hauteur du nid d'abeilles sur les propriétés élastiques. Les courbes des modules obtenues avec le modèle proposé sont bien bornées par les valeurs obtenues avec la théorie des poutres. Les contraintes d'interface sont également étudiées afin de comparer avec les modèles existant pour le problème de traction. De nombreux calculs numériques ont été réalisés avec nos H-modèles pour les problèmes de tractions, de flexions, de traction-flexion couplés, de cisaillement dans le plan, de cisaillement transversal et de torsion. De très bon accords ont été obtenus entre les résultats issus des H-modèles et ceux issus des calculs en éléments finis de coques en maillant complètement les panneaux sandwichs. Nos H-modèles ont été appliquées aux calculs de grandes plaques sandwichs industrielles en nid d'abeilles. La comparaison desrésultats entre les H-modèles et les calculs en éléments finis de coques du logiciel Abaqus sont en très bon accord. / The aim of this thesis is to develop an analytical homogenization model for the honeycomb core sandwich panels. Unlike conventional methods, the skin effects are taken into account, leading to a very different mechanical properties. In the cases of extensions, bendings, in-plane shear, transverse shears andtorsion, different analytical function series are proposed to consider the stress redistribution between the honeycomb walls. We have studied the influence of the height of the core on its homogenized properties. The moduli curves obtained by the present H-models are well bounded by the moduli values obtained by the beam theory. The interface stresses are also studied to compare with existing models for stretching problem. Many numerical computations with our H-models have been done for the problems of stretching, bending, in-plan and transverse shearing, as well as torsion. Very good agreement has been achieved between the results of the H-models and the results obtained by finite element simulations by completely meshing thesandwich panel with shell elements. Our H-models have been applied to the computations of industrial large sandwich panels with honeycomb core. The comparison of the results between the H-models and the simulations with Abaqus shell elements are in very good agreement.

The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without torsion at each node and create identical angles between any two neighbors. (3) The design of polyhedral patterns on freeform surfaces, which are aesthetic designs created by planar panels. (4) The design of space frame structures that are statically-sound and material-e cient structures constructed by connected beams. Rationalization of cross sections of beams aims at minimizing production cost and ensuring force equilibrium as a functional constraint.

In this dissertation I present advances in the studies of artificial lattices with honeycomb topology, called artificial graphene (AG), in nano-patterned GaAs quantum wells (QWs). AG lattices with very small lattice constants as low as 40 nm are achieved for the first time in GaAs. The high quality AG lattices are created by optimized electron-beam (E-beam) lithography followed by inductively coupled plasma reactive-ion etching (ICP-RIE) process. E-beam lithography is used to define a honeycomb lattice etch mask on the surface of the GaAs QW sample and the optimized anisotropic ICP-RIE process is developed to transfer the pattern into the sample and create the AG lattices. Such high-resolution AG lattices with small lattice constants are essential to form AG miniband structures and create well-developed Dirac cones. Characterization of electron states in the nanofabricated artificial lattices is by optical experiments. Optical emission (photoluminescence) yields a determination of the Fermi energy of the electrons. A significant reduction of the Fermi energy is due to the nano-patterning process. Resonant inelastic light scattering (RILS) spectra reveal novel transitions related to the electron band structures of the AG lattices. These transitions exhibit a remarkable agreement with the predicted joint density of states (JDOS) based on the band structure calculation for the honeycomb topology. I calculate the electron band structures of AG lattices in nano-patterned GaAs QWs using a periodic muffin-tin potential model. The evaluations predict linear energy-momentum dispersion and Dirac cones, where the massless Dirac fermions (MDFs) appear, occur in the band structures. Requirements of the parameters of the AG potential to achieve isolated and well-developed Dirac cones are discussed. Density of states (DOS) and JDOS from AG band structures are calculated, which provide a basis to interpret quantitatively observed transitions of electrons involving AG bands. RILS of intersubband transitions reveal intriguing satellite peaks that are not present in the as-grown QWs. These additional peaks are interpreted as combined intersubband transitions with simultaneous change of QW subband and AG band index. The calculated JDOS for the electron transitions within the AG lattice model provide a remarkably accurate description of the combined intersubband excitations. Novel low-lying excitation peaks in RILS spectra, interpreted as direct transitions between AG bands without change in QW subband, provide a more direct insight on the AG band structures. We discovered that RILS transitions around the Dirac cones are resonantly enhanced by varying the incident photon energies. The spectral lineshape of these transitions provides insights into the formation of Dirac cones that are characteristic of the honeycomb symmetry of the AG lattices. The results confirm the formation of AG miniband structures and well-developed Dirac cones. The realization of AG lattices in a nanofabricated high mobility semiconductor offers the advantage of tunability through methods suitable for device scalability and integration. The last part of this thesis describes the growth of nanocrystalline single layer and bilayer graphene on sapphire substrates by molecular beam epitaxy (MBE) with a solid carbon source. Raman spectroscopy reveals that fabrication of single layer, bilayer or multilayer graphene crucially depends on MBE growth conditions. Etch pits revealed by atomic force microscopy indicate a removal mechanism of carbon by reduction of sapphire. Tuning the interplay between carbon deposition and its removal, by varying the incident carbon flux and substrate temperature, should enable the growth of high quality graphene layers on large area sapphire substrates.

Omnipresence of heterogeneity is conspicuous in all creations of nature. Heterogeneity manifests itself in many forms at different scales, both in time and space. Engineering domain being an exotic fusion of human creativity and ever-increasing demands exemplifies the ubiquity of heterogeneity. Surprisingly, the plethora of materials we see around seem to stem from myriad combination of few base materials identified as elements in chemistry. Further, a simple rearrangement of atoms in these materials leads to allotropes with startling contrasts in properties. Similarly, micro- and meso-scales in heterogeneous materials also dis-play this phenomenon. Human requirements propelled by necessities and wants have leveraged heterogeneity deliberately or naively. In the context of engineering materials, light weight heterogeneous materials like composites and cellular solids are outstanding inventions from the last century. The present thesis highlights this phenomenon on a meso-scale to explore generalized variants of circular and elliptical honeycomb structures (HCSs) with an emphasis on their effective transverse elastic responses, a crucial pillar of engineering design and analysis. Homogenized or effective properties are an extension of continuum hypothesis, conceived for ease in analyses. E ective properties are employed in multi-scale analyses resulting in less complex models for analysis, for example, for predicting the speed of wave propogation. The thesis extends and generalizes existing close-packed circular and elliptical HCSs to more broader configurations. Simpler periodic arrangement of the unit cells from numerous exotic possibilities directly incorporates Design for Manufacture and Assembly (DFMA) philosophy and o ers a potential scope for analysis by simpler tools resulting in handy expressions which are of great utility for designer engineers. In this regard, analytical expressions for moduli having compact forms in the case of circular HCS are developed by technical theories and rigorous theory of elasticity. Regression analysis expressions for the moduli of elliptical HCS are presented, and the elasticity solutions for the same are highlighted. The thesis consists of seven chapters with Chapter 1 presenting generalized circular and elliptical HCSs as a potential avenue beyond composite materials. Following a survey of pertinent HCS literature of these HCSs, research gaps and scope are delineated. Chapter 2 briefly y summarizes the ideas, concepts and tools including analytical and numerical methods. This chapter sets the ground for the analysis of generalized circular and elliptical HCS in the following four chapters. Following the classification of the circular HCSs, Chapter 3 assesses the complete transverse elastic responses of generalized circular HCS through technical theories which are a first-order approximation. Here, thin ring theory and the more elaborate curved beam theory are employed as models to assess the moduli. Normal moduli - E and - are obtained by employing Castigliano method, while shear moduli (G ) are obtained by solving the differential equations derived in terms of displacements. Compact expressions for moduli presented wherever possible furnish the designer with a range of moduli for different configurations and modular ratios (Ey=Ex). The results show the range of applicability of technical theories within 5% of FEA. For hexagonal arrays, these results are more refined than those in literature; while the same are new for other configurations. Surprisingly, the more elaborate curved beam theory offers no better results than the thin ring theory. Chapter 4 extends the aforementioned task of assessing the complete trans-verse elastic moduli of generalized circular HCS by employing rigorous theory of elasticity (TOE) which is a second-order approximation. Utilizing Airy stress function in polar coordinates, the boundary value problems resulting from modeling of the circular HCS under different loads are solved analytically in conjunction with FEA employing contact elements. Contact elements circumvent the point loads which give finite values of displacements in technical theories and singular values in TOE. A widely used idea of employing distributed load, statically equivalent to point load, is invoked to empower TOE. The distributed load is assumed a priori and the contact length is obtained from FEA employing con-tact elements. Thus, FEA compliments the present analytical methods. Results demonstrate a very good match between analytical method in conjunction with FEA and numerical results from FEA; the error is within 5% for very thick ring (thickness-radius ratio 0.5). Further, computationally and numerically efficient expressions for displacements give better results with same computational facility. To illustrate the effect of coating on effective moduli, a limited study based on thin ring theory and elasticity theories is undertaken in Chapter 4. The study explores the effects of moduli and thickness ratios of substrate to coating on the effective normal moduli. Employing thin ring theory with only flexure as the bending mode, we get compact expressions giving good match for very thin rings in all confifigurations. The elasticity approach presented for square array demonstrates a very good match with FEA for thick rings. Coatings offer a strategy to increase the effective moduli with same dimensions. Chapter 5 broadens the scope of circular HCS by considering elliptical HCSs. While generalized circular HCS can cater to anisotropic requirement to an extent, larger spectrum is offered by considering elliptical honeycomb structures. In this regard, a generalized version of concentric thin coated elliptical HCS is investigated for transverse moduli. Thin HCSs are explored by technical theories as in circular HCS. However, a lack of exact compact-form expressions necessitates the use of regression analysis. The resulting expressions are presented in terms of ellipticity ratio describing the ovality of the ellipse and geometric parameters. Normal moduli are obtained by Castigliano method implemented in MATHE-MATICA, but shear moduli are obtained from FEA employing beam elements. The need for FEA employing beam elements stems from the subtle fact that Castigliano method implicitly assumes preclusion of rigid body motions, while shear loading for shear moduli evaluation entails rigid body motions. Interestingly, curved beam theory, as in circular HCS, offers no better refinement in assessing the moduli as compared to thin ring theory. The graphs showing the moduli with respect to thickness and modular ratios are presented as design maps to aid the designer. Chapter 6 extends the works of thin concentric coated elliptical to thicker concentric and a novel confocal elliptical HCS, a variant of elliptical HCS. In this regard, thick concentric and confocal elliptical HCS by elasticity approach are attempted for a simple case. Airy stress function in polar coordinates is tried for concentric elliptical HCS. Confocal HCS analysis employs stress function in terms of elliptical coordinate system. After proving the correctness of the stress function for both the cases by comparing the reconstructed boundary conditions with actual boundary conditions, the restrictions in solving the case of rings under load over a small region is highlighted. A parametric study for moduli is under-taken by employing FEA. These are presented as design graphs which compare and contrast the two variants of elliptical HCS on the same graphs. The modular ratio (Ey=Ex) is conspicuously more for confocal elliptical HCS than concentric elliptical HCS. Chapter 7 gives the conclusions in a nutshell, and explores the feasibility of stress evaluation of heterogeneous media on the lines of effective media theory.

Die neuen Fertigungsmöglichkeiten durch die Additive Fertigung ermöglicht es nicht nur topologisch neuartige Bauteile herzustellen, sondern auch Bauteile mit inneren Strukturen zu versehen, die der Bauteilbelastung angepasst sind oder anderen Funktionen Freiräume bieten. Ein Ansatz ist es durchlässige innere Strukturen, z. B. Gitterstrukturen (auch als Lattice Strukturen bezeichnet) einzusetzen und durch die damit geschaffenen großen inneren Flächen eine effiziente Bauteilkühlung zu realisieren. Anhand eines einfachen Beispiels wird durch Simulation und Experiment die Wirkung einer solchen Kühlung gezeigt. Als weiteres Anwendungsbeispiel wird der Einsatz verschiedener innere Strukturen zur festigkeitsgerechten Gestaltung gewichtsoptimierter Bauteile vorgestellt. In beiden Fällen wird die Gestaltung mit Hilfe von FE-Modellen experimentell begleitet. / The new manufacturing possibilities offered by additive manufacturing not only allows to produce topologically novel components, but also enables to provide components with internal structures that are adapted to the component load or offer new possibilities for other functions. One approach is to use permeable internal structures, e. g. lattice structures, to realize efficient component cooling through the large internal surfaces created thereby. The effect of such a cooling is demonstrated by simulations and experiments using a simple example. As a further application example, the use of various internal structures for the strength-oriented design of weight-optimized components will be presented. In both cases the design is experimentally accompanied by FE models.