Cellular materials are often used as impact/blast attenuators due to their capacity to absorb kinetic energy when compressed to large strains. For such applications, three key material properties are the crushing stress, plateau stress and densification strain. The difficulties associated with obtaining these mechanical properties from dynamic/impact tests are outlined. The results of an experimental investigation of the quasi-static and dynamic mechanical properties of two types of cellular materials are reported.The dynamic tests were carried out using Hopkinson pressure bars. Experimentally determined propagation coefficients are employed to represent both dispersion and attenuation effects as stress waves travel along the bars. Propagation coefficients were determined for 20 mm and 40 mm diameter viscoelastic PMMA pressure bars and for elastic Magnesium pressure bars. The use of the elementary wave theory is shown to give satisfactory results for frequencies of up to approximately 15 kHz, 8 kHz and 30 kHz for the 20 mm and 40 mm diameter PMMA bars and the 23 mm diameter Magnesium bars respectively. The use of low impedance, viscoelastic pressure bars is shown to be preferable for testing low density, low strength materials.The quasi-static and dynamic compressive properties of balsa wood, Rohacell-51WF and Rohacell-110WF foams are investigated along all three principal directions. The dynamic properties were investigated by performing Split Hopkinson Pressure Bar (SHPB) and Direct Impact (DI) tests. In general, the crushing stress, the plateau stress and the densification strain remain constant with increasing strain rate of the SHPB tests. However, a dynamic enhancement of the crushing stress and plateau stress was revealed for balsa wood and Rohacell-51WF. In contrast, the plateau stresses of the Rohacell-110WF specimens are lower for SHPB than quasi-static tests. From the DI tests, it is shown that compaction waves have negligible effect on the stresses during dynamic compaction of along and across the grain balsa wood at impact speeds between approximately 20-100 m/s. Alternatively, the proximal end stresses of both Rohacell-51WF and 110WF foams increase with increasing impact velocity, following the quadratic trend predicted by 'shock theory'. This indicates that compaction waves are important for the case of Rohacell foam, even at low impact velocities.

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The cellular nature of many biological materials, providing them with low density, high strength and high toughness, have fascinated many researchers in the field of botany and structural biology since at least one century. Bamboo, sponges, trabecular bone, tooth and honeybee combs are only few examples of natural materials with cellular architecture. It has been widely recognised that the geometric and mechanical characteristics of the microscopic building blocks play a fundamental role on the behavior observed at the macroscale. Up to date, many efforts have been devoted to the analysis of cellular materials with empty cells to predict the structure-property relations that link the macroscopic properties to the mechanics of their underlying microstructure. Surprisingly, notwithstanding the great advantages of the composite solutions in nature, in the literature a limited number of investigations concern cellular structures having the internal volumes of the cells filled with fluids, fibers or other bulk materials as commonly happens in biology. In particular, a continuum model has not been derived and explicit formulas for the effective elastic constants and constitutive relations are currently not available. To provide a contribution in this limitedly explored research area, this thesis describes the mathematical formulation and modelling technique leading to explicit expressions for the macroscopic elastic constants and stress-strain relations of biologically inspired composite cellular materials. Two examples are included. The first deals with a regular hexagonal architecture inspired by the biological parenchyma tissue. The second concerns a mutable cellular structure, composed by mutable elongated hexagonal cells, inspired by the hygroscopic keel tissue of the ice plant Delosperma nakurense. In both cases, the predicted results are found to be in very good agreement with the available data in the literature. Then, by taking into account the benefits offered by the complex hierarchical organisation of many natural systems, the attention is focused on the potential value of adding structural hierarchy into two-dimensional composite cellular materials having a self-similar hierarchical architecture, in the first case, and different levels with different cell topologies, in the second. In contrast to the traditional cellular materials with empty cells, the analysis reveals that, in the cell-filled configuration, introducing levels of hierarchy leads to an improvement in the specific stiffness. Finally, to offer concrete and relevant tools to engineers for developing future generations of materials with enhanced performance and unusual functionalities, a novel strategy to obtain a honeycomb with mutable cells is proposed. The technique, based on the ancient Japanese art of kirigami, consists in creating a pattern of cuts into a flat sheet of starting material, which is then stretched to give a honeycomb architecture. It emerges a vast range of effective constants that the so-called kirigami honeycomb structures can be designed with, just by changing the value of the applied stretch.

Several metal honeycombs, termed Linear Cellular Alloys (LCAs), were fabricated via a paste extrusion process and thermal treatment. Two Fe-Ni based alloy compositions were evaluated. Maraging steel and Super Invar were chosen for their compatibility with the process and the wide range of properties they afforded. Cell wall material was characterized and compared to wrought alloy specifications. The bulk alloy was found to compare well with the more conventionally produced wrought product when porosity was taken into account. The presence of extrusion defects and raw material impurities were shown to degrade properties with respect to wrought alloys. The performance of LCAs was investigated for several alloys and cell morphologies. The results showed that out-of-plane properties exceeded model predictions and in-plane properties fell short due to missing cell walls and similar defects. Strength was shown to outperform several existing cellular metals by as much as an order of magnitude in some instances. Energy absorption of these materials was shown to exceed 150 J/cc at strains of 50% for high strength alloys. Finally, the suitability of LCAs as an energetic capsule was investigated. The investigation found that the LCAs added significant static strength and as much as three to five times improvement in the dynamic strength of the system. More importantly, it was shown that the pressures achieved with the LCA capsule were significantly higher than the energetic material could achieve alone. High pressures, approaching 3 GPa, coupled with the fragmentation of the capsule during impact increased the likelihood of initiation and propagation of the energetic reaction. This multi-functional aspect of the LCA makes it a suitable capsule material.

This work investigates the application of homogenization techniques to the dynamic analysis of periodic solids, with emphasis on lattice structures. The presented analysis is conducted both through a Fourier-based technique and through an alternative approach involving Taylor series expansions directly performed in the spatial domain in conjunction with a finite element formulation of the lattice unit cell. The challenge of increasing the accuracy and the range of applicability of the existing homogenization methods is addressed with various techniques. Among them, a multi-cell homogenization is introduced to extend the region of good approximation of the methods to include the short wavelength limit. The continuous partial differential equations resulting from the homogenization process are also used to estimate equivalent mechanical properties of lattices with various internal configurations. In particular, a detailed investigation is conducted on the in-plane behavior of hexagonal and re-entrant honeycombs, for which both static properties and wave propagation characteristics are retrieved by applying the proposed techniques. The analysis of wave propagation in homogenized media is furthermore investigated by means of the bridging scales method to address the problem of modelling travelling waves in homogenized media with localized discontinuities. This multi-scale approach reduces the computational cost associated with a detailed finite element analysis conducted over the entire domain and yields considerable savings in CPU time. The combined use of homogenization and bridging method is suggested as a powerful tool for fast and accurate wave simulation and its potentials for NDE applications are discussed.

Passive plant actuators have fascinated many researchers in the field of botany and structural biology since at least one century. Up to date, the most investigated tissue types in plant and artificial passive actuators are fibre-reinforced composites (and multilayered assemblies thereof) where stiff, almost inextensible cellulose microfibrils direct the otherwise isotropic swelling of a matrix. In addition, Nature provides examples of actuating systems based on lignified, low-swelling, cellular solids enclosing a high-swelling cellulosic phase. This is the case of the Delosperma nakurense seed capsule, in which a specialized tissue promotes the reversible opening of the capsule upon wetting. This tissue has a diamond-shaped honeycomb microstructure characterized by high geometrical anisotropy: when the cellulosic phase swells inside this constraining structure, the tissue deforms up to four times in one principal direction while maintaining its original dimension in the other. Inspired by the example of the Delosoperma nakurense, in this thesis we analyze the role of architecture of 2D cellular solids as models for natural hygromorphs. To start off, we consider a simple fluid pressure acting in the cells and try to assess the influence of several architectural parameters onto their mechanical actuation. Since internal pressurization is a configurational type of load (that is the load direction is not fixed but it “follows” the structure as it deforms) it will result in the cellular structure acquiring a “spontaneous” shape. This shape is independent of the load but just depends on the architectural characteristics of the cells making up the structure itself. Whereas regular convex tiled cellular solids (such as hexagonal, triangular or square lattices) deform isotropically upon pressurization, we show through finite element simulations that by introducing anisotropic and non-convex, reentrant tiling large expansions can be achieved in each individual cell. The influence of geometrical anisotropy onto the expansion behaviour of a diamond shaped honeycomb is assessed by FEM calculations and a Born lattice approximation. We found that anisotropic expansions (eigenstrains) comparable to those observed in the keels tissue of the Delosoperma nakurense are possible. In particular these depend on the relative contributions of bending and stretching of the beams building up the honeycomb. Moreover, by varying the walls’ Young modulus E and internal pressure p we found that both the eigenstrains and 2D elastic moduli scale with the ratio p/E. Therefore the potential of these pressurized structures as soft actuators is outlined. This approach was extended by considering several 2D cellular solids based on two types of non-convex cells. Each honeycomb is build as a lattice made of only one non-convex cell. Compared to usual honeycombs, these lattices have kinked walls between neighbouring cells which offers a hidden length scale allowing large directed deformations. By comparing the area expansion in all lattices, we were able to show that less convex cells are prone to achieve larger area expansions, but the direction in which the material expands is variable and depends on the local cell’s connectivity. This has repercussions both at the macroscopic (lattice level) and microscopic (cells level) scales. At the macroscopic scale, these non-convex lattices can experience large anisotropic (similarly to the diamond shaped honeycomb) or perfectly isotropic principal expansions, large shearing deformations or a mixed behaviour. Moreover, lattices that at the macroscopic scale expand similarly can show quite different microscopic deformation patterns that include zig-zag motions and radical changes of the initial cell shape. Depending on the lattice architecture, the microscopic deformations of the individual cells can be equal or not, so that they can build up or mutually compensate and hence give rise to the aforementioned variety of macroscopic behaviours. Interestingly, simple geometrical arguments involving the undeformed cell shape and its local connectivity enable to predict the results of the FE simulations. Motivated by the results of the simulations, we also created experimental 3D printed models of such actuating structures. When swollen, the models undergo substantial deformation with deformation patterns qualitatively following those predicted by the simulations. This work highlights how the internal architecture of a swellable cellular solid can lead to complex shape changes which may be useful in the fields of soft robotics or morphing structures. / Passive pflanzliche Aktuatoren sind bewegliche Strukturen, die eine komplexe Bewegung ohne jegliche metabolische Energiequelle erzeugen können. Diese Fähigkeit entstammt dabei der Materialverteilung mit unterschiedlicher Quellbarkeit innerhalb der Gewebsstruktur.Die bis heute am besten untersuchten Gewebearten pflanzlicher und künstlicher Passivaktuatoren sind Faserverbundwerkstoffe, in denen steife, fast undehnbare Zellulosemikrofibrillen die ansonsten isotrope Schwellung einer Matrix leiten. Darüber hinaus gibt es in der Natur Beispiele für Aktuationssysteme, wie z.B. die Delosoperma nakurense Samenkapsel, in der das Aktuatorgewebe eine Wabenstruktur aufweist, deren Zellen mit einem hochquellenden Material gefüllt sind. Dabei hat die Wabenstruktur des Gewebes eine hohe geometrische Anisotropie, so dass sich das Gewebe bei Wasseraufnahme bis zur vierfachen Länge entlang einer Hauptrichtung ausdehnt und somit die reversible Öffnung der Kapsel angetrieben wird. Inspiriert durch das Vorbild der Delosoperma nakurense, wird in der vorliegenden Arbeit die Rolle der Architektur von 2D-Zellulärmaterialien als Modell für natürliche passive Aktuatoren analysiert. Zunächst wird anhand eines einfachen Flüssigkeitsdrucks in den Zellen der Einfluss verschiedener architektonischer Parameter auf deren mechanische Betätigung untersucht. Wohingegen regelmäßige konvexe Wabenstrukturen (wie z. B. sechseckige, dreieckige oder quadratische Gitter) sich unter Druck isotropisch verformen, wird durch Finite-Elemente-Simulationen gezeigt, dass es bei anisotropen und nicht-konvexen Zellen zu großen Ausdehnungen jeder einzelnen Zelle kommt. Auch wenn nur eine einzelne Zellgeometrie betrachtet wird, können hierbei viele verschiedene Gitter entstehen. Die Ausdehnungsrichtung des Gitters ist variabel und hängt von der lokalen Konnektivität der Zellen ab. Dies hat Auswirkungen sowohl auf makroskopischer (Gitter-) als auch auf mikroskopischer (Zell-) Ebene. Auf makroskopischer Ebene erfahren diese nicht-konvexen Gitter entweder große anisotrope (ähnlich der Delosperma nakurense Samenkapsel) oder vollkommen isotrope Eigendehnungen, große Scherverformungen oder jeweilige Mischformen. Überdies können Gitter mit ähnlichem makroskopischem Verhalten gänzlich unterschiedliche mikroskopische Verformungsmuster zeigen, wie z.B. Zick-Zack-Bewegungen oder radikale Änderungen der ursprünglichen Zellform. Dies verursacht auch eine entsprechende Änderung der elastischen Eigenschaften. In Abhängigkeit der Gitterarchitektur kann es zu gleichen oder unterschiedlichen mikroskopischen Zelldeformationen kommen, die sich in Summe entweder verstärken oder ausgleichen, und somit die Vielzahl an makroskopischen Verhalten erklären. Interessanterweise lassen sich mit Hilfe einfacher geometrischer Argumente aus der nichtdeformierten Zellform und Zellkonnektivität die Ergebnisse der FE-Simulationen vorhersagen. Die Ergebnisse der Finite-Elemente-Simulationen wurden durch Laborversuche bestätigt, in denen (mit 3D-Drucktechnik gefertigte) Modellgitter ähnliches Ausdehnungsverhalten beim Quellen zeigen. Diese Arbeit zeigt auf, wie die Innenarchitektur eines quellfähigen zellulären Feststoffs zu komplexen Formänderungen führen kann, die in den Bereichen der Soft-Robotik oder bei Morphing-Strukturen angewandt werden können.

Microtruss materials are assemblies of struts or columns arranged periodically in space. The majority of past research efforts have focused on the key issue of microtruss architectural optimization. By contrast, this study focuses on the internal material structure at the level of the individual struts. Microstructural, geometrical, and material design techniques are used to improve their mechanical properties. The finite element method is used to verify and create predictive analytical models, explain the dependence of strut properties on geometry, material properties and failure mechanisms, and extend the strut design analysis into suggestions for the improvement of fabrication methods. Three strut design methods are considered. First, microstructural design is performed by considering the influence of strut geometry on the strain energy imparted during stretch bending. By using the perforation geometry to modify the location and magnitude of this strain energy, microtruss materials with lower density and higher strength can be fabricated. Second, structural sleeves of aluminum oxide and electrodeposited nanocrystalline nickel are used to reinforce architecturally optimized aluminum alloy microtruss assemblies, creating hybrid materials with high weight-specific strength. The mechanical properties are controlled by the interaction between material and mechanical failure; this interaction is studied through finite element analyses and a proposed analytical relationship to provide suggestions for further improvements. Finally, hollow cylindrical struts are fabricated from electrodeposited nanocrystalline nickel. The high strength to weight ratio achieved in these struts is due to the microstructural and cross-sectional efficiency of the material.

Microtruss materials are assemblies of struts or columns arranged periodically in space. The majority of past research efforts have focused on the key issue of microtruss architectural optimization. By contrast, this study focuses on the internal material structure at the level of the individual struts. Microstructural, geometrical, and material design techniques are used to improve their mechanical properties. The finite element method is used to verify and create predictive analytical models, explain the dependence of strut properties on geometry, material properties and failure mechanisms, and extend the strut design analysis into suggestions for the improvement of fabrication methods. Three strut design methods are considered. First, microstructural design is performed by considering the influence of strut geometry on the strain energy imparted during stretch bending. By using the perforation geometry to modify the location and magnitude of this strain energy, microtruss materials with lower density and higher strength can be fabricated. Second, structural sleeves of aluminum oxide and electrodeposited nanocrystalline nickel are used to reinforce architecturally optimized aluminum alloy microtruss assemblies, creating hybrid materials with high weight-specific strength. The mechanical properties are controlled by the interaction between material and mechanical failure; this interaction is studied through finite element analyses and a proposed analytical relationship to provide suggestions for further improvements. Finally, hollow cylindrical struts are fabricated from electrodeposited nanocrystalline nickel. The high strength to weight ratio achieved in these struts is due to the microstructural and cross-sectional efficiency of the material.

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 thesis presents a detailed experimental programme on understanding the mechanics of drilling in porous brittle solids. Gypsum was used as a model material for this experimental study, in which the mechanics of drilling was decoupled into equivalent problems of indentation and cutting. A comprehensive understanding of the mechanics of indentation and cutting was gained by performing experiments in 2-D conditions. A camera and microscope assembly was used to capture images at high temporal and spatial resolution to measure the in situ deformation. Particle image velocimetry (PIV) algorithm was used to measure the deformation parameters such as velocity, strain-rate, strain and volume change. In the last part of this research, drilling experiments were performed in 3-D conditions and an attempt was made for understanding the mechanics of drilling by relating the drilling experiment results to that of indentation and cutting. A series of wedge indentation experiments were performed under 2-D plane-strain conditions. Development of a parabolic zone of deformation, surrounding the indenter, was observed, wherein this size of the deformation zone and the strain accumulation in the deformation zone was a function of the geometry of the indenter. The maximum effective strain decreased and the overall strain field was more diffuse with increase in the wedge angle. Significant volume change was also observed in this deformation zone and the amount of volume change increased with increase in the porosity of the material. The zones of high volume change (compaction bands) were stacked in the form of layers oriented perpendicular to the direction of indentation. These compaction bands were more localized for the case of lower angles of wedge indenter. The extent of the compaction bands was also a function of porosity and spread over a larger area for the case of low porosity samples. A change in the material response was also observed with change in porosity and geometry of the indenter. The appearance of the crack was delayed with increase in porosity and reduction of wedge angle. The experimental results were also used to validate an analytical cavity expansion model. A better prediction of indentation pressure and the size of the deformation zone was possible after volume change corrections were incorporated into the cavity expansion formulation. A series of orthogonal cutting experiments were performed in 2-D plane-strain conditions. The e ect of tool geometry and the depth of cut on the mechanics of cutting was studied with the help of image based measurements and cutting force signatures. Different types of cutting mechanisms were observed for the case of positive and negative rake angle tool. A cyclic increase and decrease in the cutting force was observed in case of positive rake angle cutting tool. The decrease in the cutting force corresponded to the initiation of crack from the tip of the tool. The crack traversed towards the surface of the material and resulted in the removal of a material chip. With progress of cutting, the tool scratched the material surface, giving rise to the gradual increase in the cutting force as it again reached local maxima when the tool completely re-engaged with the material. For the case of negative rake angle, apart from cyclic increase and decrease of the cutting force, there was a development of a triangular dead zone at the tip of the cutting tool. The size of the dead zone varied cyclically with the progress of cutting. The length of crack, which resulted in the removal of the chip from the material, was found to be a function of the rake angle and the depth of cut. Drilling experiments were performed on gypsum samples in 3-D conditions. Two types of twist drills with different helix angles were used for this research work. Experiments were performed on the samples with two different porosities. Thrust force and torque signatures were recorded for five values of depth of cut per revolution. Since these experiments were performed in 3-D, image analysis was not performed. However, in order to ascertain a qualitative understanding of the drilling process, few experiments were performed on the edge of the material surface so that a cylindrical groove with semicircular cross section is made and the exposed surface of the material and the drill were imaged. The normalized thrust force and normalized torque were compared with indentation pressure and cutting force signatures and remarkable similarities between them was found. A transition from ductile to brittle type of response was observed with increase in the depth of cut per revolution, which was similar to what was observed in case of indentation. The magnitude of torque was found to be higher for high helix angle drills, which was counter to what was observed in cutting, which was due to the deposition of the material in helix for high helix angle drills, resulting in the reduction of the effective helix angle. An approximate estimate of the effective helix angle was made with the help of analytical solutions as well as from the qualitative analysis of the images.