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This thesis considers the modelling of two and three dimensional molecular networks with a view to being able to predict how the geometry of a network will affect the elastic constants and specifically the Poisson's ratios of the network. Materials with negative Poisson's ratios have much better engineering properties then those with positive Poisson's ratios. Theory states that a network polymer, with negative Poisson's ratios at a molecular level, would have much better properties than most materials with negative Poisson's ratios made to date. Molecular modelling has been used to examine the elastic constants of those two and three dimensional network polymers which are most likely to be synthesised in the near future. Such networks have been predicted to have either large positive or large negative Poisson's ratios depending on the molecular arrangement of the network. Poisson's ratios varying between 0.96 and -0.86 for the three dimensional cases and between -0.9 and 1.26 for the two dimensional cases have been calculated. Young's moduli in the order of 1 GPa have been observed for the three dimensional networks as compared to Young's moduli in the order of 20 - 400 kPa which have been experimentally measured for foam materials. Comparison with local density functional calculations for two 2-D networks with the molecular modelling have confirmed the negative Poisson's ratio in these networks and shown that it is not a function of the molecular modelling packages or force field used. The off-axis properties for both the two and three dimensional networks have been calculated. These show that whilst the networks with a positive Poisson's ratio in the principal axis directions always have a positive Poisson's ratio, those networks with a negative Poisson's ratio in the principal axis directions have off-axis Poisson's ratios that vary between large and positive and large and negative. In general the networks with positive Poisson's ratios are much more isotropic than those with negative Poisson's ratios. Analytical models which model the networks using simple beam theory have been produced for various two and three dimensional networks. These models can be used to predict the elastic constants of a network without the need to do time consumingmolecular modelling calculations to a first approximation. Comparison of the molecular models and analytical models has led to the development a library of force constants for two dimensional networks which can be used to more accurately predict the elastic constants of a network based on a knowledge of the geometry of the network and the constituent `sub-units' from which it is made

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Negative Linear Compressibility (NLC), where a material expands in a given direction when subjected to hydrostatic compression, is a rare elastic property that has received much attention recently, but has yet to be used in practical applications. What are the mechanisms responsible for this property in crystals and man-made structures? Are all mechanisms somehow related to the wine-rack model? Can we find an even simpler and more fundamental elucidation of NLC? Following this mechanistic approach, can we then identify “engineering” materials with NLC? To answer these questions, I have used a combination of analytical modelling based on beam theory and finite element analysis, to investigate several structures. At first, I examine in great detail the standard wine-rack in 2D and equivalents in 3D and identify the aspect ratio (close to two) at which NLC is maximum. By adding spacers I demonstrate that a cross is not a necessary condition, and that simpler angle changes in chains are sufficient to generate NLC. Looking for materials with intersecting straight chains, “zig-zag” chains or quasi-helical structures, I find that carbon fibre mats, some extruded polymers and some woods exhibit NLC. Finally, I show that elliptical voids in 2D sheets can also generate NLC in a way related to the wine-rack. This thesis improves the understanding of the mechanism(s) responsible for NLC by proving that a wine-rack is not necessary. Perhaps more importantly it suggests that the property can be exploited in several relatively common materials.

This thesis focuses on the development, parameterization and optimization of a novel meso-scale pattern used to induce auxetic behavior, i.e., negative Poisson's ratio, at the bulk scale. Currently, the majority of auxetic structures are too porous to be utilized in conventional load-bearing applications. For others, manufacturing methods have yet to realize the meso-scale pattern. Consequently, new auxetic structures must be developed in order to confer superior thermo-mechanical responses to structures at high temperature. Additionally, patterns that take into account manufacturing limitations, while maintaining the properties characteristically attached to negative Poisson's Ratio materials, are ideal in order to utilize the potential of auxetic structures. A novel auxetic pattern is developed, numerically analyzed, and optimized via design of experiments. The parameters of the meso-structure are varied, and the bulk response is studied using finite element analysis (FEA). Various attributes of the elasto-plastic responses of the bulk structure are used as objectives to guide the optimization process

The performance of peristaltic pumps is mainly governed by their tubing or hose materials. Research and development in this area is therefore very important for peristaltic pump manufacturers to keep in front of the competition and to open up new applications to enable further market penetration. Another aspect of this is of course price; performance and cost have to be in balance. As an approach to fabricate a new tube material, the field of negative Poisson's ratio (or: auxetic) materials is explored. The combined deformations of tensile, compression and shear in a peristaltic pump tube may well benefit from the specific characteristics of auxetic materials. Materials can be designed to keep their dimensions constant in directions perpendicular to an applied load. This is referred to as “auxetic balancing”. Finite element modelling shows that lowering the Poisson's ratio will rapidly decrease the maximum stresses in the cross-section of an occluded tube. Optimum values for the Poisson's ratio are found to be between −0.1 and +0.1, preferentially being 0. The re-entrant honeycomb structure is selected for initial trials, but manufacturing of this structure at the desired dimension proved to be too difficult at this time. Instead, electrospun nanofibre membranes are selected as the reinforcement structure. A liquid silicone elastomer is used as the matrix material. Key characteristics for the new material are derived from baseline test results on existing tubing. Laminates are manufactured from electrospun nylon6 nanofibre membranes coated with a liquid silicone rubber. Compression moulding is used to cure the nylon6-silicone rubber laminate, to give two effects: it ensures impregnation of the membrane and the compression deforms the nanofibre structure in such a way that it will become auxetic through-the-thickness. Flat sheet laminates of 2 mm thickness are manufactured with 14 layers of reinforcement. A reinforcing effect and substantial lowering of the through-the-thickness Poisson's ratio is observed for the laminates at low strains. At higher strains (>50%) the effect of the reinforcement diminishes and the Poisson's ratio of the laminate and pure silicone rubber equalises. Finally, tubular laminates are manufactured and the resulting tubes are tested in a peristaltic pump with some promising results (>1 million occlusions before failure). Tube performance is not yet at the required level, but with further optimisation of the laminating process, mould design and (post-)curing large steps forward can be made.

Digital light Projection based Additive Manufacturing (AM) enables fabrication of complex three-dimensional (3D) geometries for applications ranging from rapid prototyping jet parts to scaffolds for cell cultures. Despite the ability in producing complex, three-dimensional architectures, the state of art DLP AM systems is limited to a single homogenous photo-polymer and it requires a large volume of resin bath to begin with. Extensible Multi-material Stereolithography (EMSL) is a novel high-resolution projection stereolithography system capable of manufacturing hybrid 3D objects. This system provides new capabilities, allowing more flexible design criteria through the incorporation of multiple feedstock materials throughout the structure. With EMSL manufacturing ability, multi-material programmable negative Poissons ratio honeycomb reentrant structures are realized. Researchers have been studying auxetic structures over decades, the mechanical property control of auxetic structure mainly relies on geometry design in previous studies. Now with the help of EMSL system, other design variables associated with auxetic structures, such as material properties of local structural members, are added into design process. The additional variables are then proved to have significant effects on the material properties of the auxetic structures. The ability to accurately manufacture multi-material digital design will not only allow for novel mechanical and material researches in laboratory, but also extend the additive manufacturing technology to numerous future applications with characteristics such as multiple electrical, electromechanical and biological properties. The design and optimization of EMSL system realizes novel structures have not been producible, therefore it will stimulate new possibilities for future additive manufacturing development. / Master of Science

Methods to mitigate the risk posed by seismic and blast loads to structures are of high interest to researchers. Auxetic structures are a new class of metamaterials that exhibit counterintuitive negative Poisson's ratio (NPR) behavior based on their geometric configuration. Cellular auxetics are light-weight and cost-effective materials that have the potential to demonstrate high strength and resilience under axial forces. Existing research on metallic auxetics is scarce and based mostly on analytical studies. Apparent NPR behavior of auxetics has also been linked to enhanced energy absorbing potential. A pilot study was undertaken to investigate and understand auxetic behavior in tubes constructed using ductile metals commonly found in structural applications i.e. steel and aluminum. The main objective was to establish whether performance enhancements could be obtained through auxetic behavior in ductile metal tubes. In addition, any potential benefits to auxetic performance due to base material plasticity were studied. These objectives were fulfilled by conducting an experimental and analytical investigation, the results of which are presented in this thesis. The experimental program consisted of establishing a design methodology, manufacturing, and laboratory testing for tubular metallic specimens. A total of eight specimens were designed and manufactured comprising five steel and three aluminum. For each base metal, three different geometric configurations of cells were designed: one with a rectangular array of circular voids and two with void geometries based on the collapsed shape of circular cells in a design tube under uniaxial compressive stress. A parameter called the Deformation Ratio (DR) was introduced to quantify cell geometry. Designed tubes were manufactured via a six-axis laser cutting process. A custom-made test assembly was constructed and specimens were tested under reverse-cyclic uniaxial loading, with one exception. Digital Image Correlation (DIC) was used to acquire experimental strain data. The performance of the auxetic and non-auxetic tubular structures was evaluated based on the axial load-deformation characteristics, global deformations, and the specific energy absorption of the test specimens. The experimental test results confirmed that ductile metal tubes with special collapsed cell geometries were capable of demonstrating auxetic behavior under the applied elastic and inelastic uniaxial strains; both tensile and compressive. Base material plasticity was observed to have an insignificant effect on the auxetic response. Experimental results suggested that the unique deformation mechanism precipitated by the auxetic cell geometries resulted in more stable deformed shapes. Stability in global deformed shapes was observed to increase with an increase in DR value. In addition, the unique auxetic mechanism demonstrated an ability to distribute radial plastic strains uniformly over the height of the auxetic pattern. As a result, plastic strains were experienced by a greater fraction of auxetic tubes; this enhanced the energy-dissipating properties of auxetic specimens in comparison to the tested non-auxetic tubes. Tubes with cell geometries associated with higher DR values exhibited greater energy absorption relative to the non-auxetic specimen. For the same base metal, auxetic specimens exhibited greater axial strength and effective strain range, when compared to their non-auxetic counterparts. The increased strength was partially attributed to the increased cell wall thickness of the auxetic specimens. However, the increased strain range was attributed to the rotation in unit cells induced by the unique auxetic geometry. Experimental test data was used to validate the finite element (FE) and simplified macromechanical modeling approaches. These methods were adopted to develop design tools capable of replicating material performance and behavior as well as accurately predicting failure loads. Load-deformation response and effective Poisson's ratio behavior was established using FE models of as-built specimens, while simplified macromechanical equations were derived based on the equilibrium of forces to compute failure loads in tension. These equations relied on pattern geometry and measured experimental unit cell deformations. It was established that the manufacturing process had a detrimental effect on the properties of the aluminum specimens. Accordingly, empirical modifications were applied to the aluminum material model to capture this effect. FE models accurately replicated load-deformation behavior for both non-auxetic and auxetic specimens. Hence, the FE modeling approach was shown to be an effective tool for predicting material properties and response in ductile metal tubes without the need for experimental testing. The simplified strength equations also described material failure with reasonable accuracy, supporting their implementation as effective design tools to gauge tube strength. It is recommended that FE models be refined further through the addition of failure criteria and damage accumulation in material models. The result of this study established that auxetic behavior could be induced in ductile metal tubes through the introduction of unique cell geometry, thereby making them highly tunable and capable of exhibiting variable mechanical properties. Owing to their deformation mechanism and NPR behavior, auxetic tubes demonstrated geometric stability at greater deformations, which highlighted their potential for use as structural elements in systems designed to deform while bearing extreme loads e.g earthquakes and blast events. Additionally, the capability of auxetic geometries to distribute strains uniformly along their length was linked to the potential development of energy-dissipating structural components. It was suggested that new knowledge acquired in this study about auxetic behavior in ductile metals could support the development of new structural systems or methods of structural control based on NPR behavior. Finally, recommendations for future research were presented, based on the expansion of research to study the effects of multiple loading regimes and parametric changes on auxeticity as well as additional mechanical characteristics e.g shear resistance. / Master of Science / Special structures known as Auxetics have been studied that exhibit counterintuitive behavior based on their geometric configuration. The novel shapes and architecture of these structures allow them to deform such that they expand laterally in tension and contract laterally in compression; a property known as negative Poisson's ratio (NPR) which is rarely observed in naturally-occurring materials. Auxetic materials demonstrate mechanical properties such as high resilience, indentation resistance, and energy-absorption. An experimental and analytical study was undertaken to explore the beneficial properties of auxetic behavior, along with the effect of inelastic deformations in ductile metal auxetics. To this end, tubular test specimens, made with steel and aluminum, were designed and manufactured. To achieve auxetic behavior, a unique array of collapsed cells was cut out from metal tubes using a laser cutting process. Subsequently, specimens were tested in the laboratory under cyclic and monotonic loads. Experimental results indicate that tubes with auxetic geometries exhibited NPR behavior and a unique deformation mechanism based on the rotation of the unit cells. Owing to this mechanism, auxetic specimens possessed greater geometric stability under applied axial deformations, when compared to the tested non-auxetic specimens. The deformation mechanism was also responsible for a uniform distribution of strains along the length of the auxetic geometry which was linked to relatively better energy absorbing capacity than the non-auxetic tubes. Developed finite element (FE) models captured the response and behavior of all specimens with good accuracy. Derived simplified strength equations were also able to calculate the ultimate tensile failure loads for all specimens accurately. Both numerical methods demonstrated the potential to be utilized as design and evaluation tools for predicting material properties. Finally, recommendations to expand research, based on metal auxetic structures, were presented to further our understanding of auxetic behavior in ductile metals and to explore its benefits under varying loading regimes. Results from this research can be used to support the design of new structural systems or methods to control existing structures by exploiting NPR properties of ductile metal auxetics. Furthermore, energy-dissipating properties of metal auxetic materials may prove to be beneficial for structural applications under extreme loading conditions such as earthquakes and blasts.

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