Materials and structures with auxetic and negative linear compressibility are of great potential to be used in many applications because of their uncommon mechanical deformation features. However, their design and manufacture are less studied as compared to their mechanical properties. The aim of this research is to explore several new approaches to the design and fabrication of cellular materials and structures with these two uncommon features. Poisson’s ratio and compressibility represent fundamental metrics to measure a material’s distortion under directional loading and hydrostatic pressure. In contrast to the stiffness and strength of materials, which exhibit several orders of difference, Poisson’s ratio varies in a very narrow range, i.e., from -1 to 0.5 for isotropic materials. For cellular materials, different values of Poisson’s ratio are obtained by designing the shape and topology of their microstructures. When Poisson’s ratio is negative, the corresponding material is called an auxetic material. When the performance of an auxetic material is dominated by its geometric features and deformation mechanisms of its microstructure and its Poisson’s ratio is rare in nature, it is called an auxetic metamaterial. A similar concept applies to materials and structures with negative compressibility. To investigate the design and fabrication of these metamaterials, the research starts with identifying the geometric bounds for buckling-induced auxetic metamaterials as an extension to previous work. Then, a new design approach is developed for metallic auxetic metamaterials triggered by new findings relating to loss of buckling-induced auxetic behaviour for metallic based microstructures. Subsequently, two new methodologies are developed to design and fabricate negative linear compressibility composite (NLC) structures. All significant findings and the effectiveness of design and fabrication approaches are validated by experiments. Following an introduction in Chapter 1, the current literature on auxetic and NLC metamaterials is reviewed in Chapter 2. In Chapter 3, development of auxetic metamaterial based on functionalization of base materials and topologies is described. In the first stage of this development, the geometric limits for buckling-induced auxetic metamaterials have been identified at both infinitesimal and finite strain. The previous investigation on buckling-induced auxetic metamaterial revealed that there is a geometric limit for its microstructure to exhibit auxetic behaviour in infinitesimal deformation. However, the limit for auxetic metamaterials undergoing large deformation significantly was different from that under small deformation and has not been reported yet. Thus the geometric limit was investigated in an elastic and infinitesimal deformation range using linear buckling analysis. At finite deformation range, experimentally validated finite element models were used to identify the geometric limits for auxetic metamaterials. Depending on the controlling parameters of the topology, the bounds were represented by a line strip for one control parameter, an area for two control parameters and spatial domain surrounded by a 3D surface for three parameters. It was found that there was a significant difference in the geometric bounds at different deformation level. This difference was critical to design auxetic metamaterials for different applications and to control their auxetic performance. In the second stage of the development, the special features of metallic auxetic metamaterials were identified and investigated as the new class of auxetics. In contrast to the elastomer-based metamaterials, metallic ones possess new features as a result of the nonlinear deformation of their metallic microstructures under large deformation. The loss of auxetic behaviour in metallic metamaterials led us to carry out a numerical and experimental study to investigate the mechanism of the observed phenomenon. During this exploration, it was found that scaling the buckling modes and changing the plasticity of metallic base material can be used to tune the performance of auxetic metallic metamaterials undergoing large plastic deformation. The effectiveness of the developed tuning method was proved through both experiments and finite element simulations. By employing this tuning method, a 2D auxetic metamaterial was developed from a regular square lattice. By altering the initial geometry of microstructure with the desired buckling with a pattern scale factor (PSF) mode, the metallic metamaterial exhibited auxetic behaviour with tuneable mechanical properties. A systematic parametric study using the validated finite element models was conducted to reveal the novel features of metallic auxetic metamaterials undergoing large plastic deformation. An analytical model was derived to capture the variation of NPR with respect to strain, PSF, and plasticity of the base material. The results of this part of study provide a useful guideline for the design of 2D metallic auxetic metamaterials for various applications. In Chapter 4, two new methodologies were developed to designing new NLC composite structures. Conventionally, materials and structures contract in all directions under a positive surrounded uniform pressure. However, some materials and structures exhibit an unusual behaviour under the application of pressure, resulting in an increase in dimension along one direction. This deformation feature is referred as the NLC. To reduce the manufacturing cost using 3D printing, a composite approach was proposed to manufacture these structures. Several new cellular composite structures with NLC composite structures were used as examples to demonstrate the effectiveness of the design approach. The test samples were manufactured using the traditional composite method with low cost. These investigations have clearly demonstrated the feasibility and effectiveness of designing and manufacturing of mechanical metamaterials using the presented approaches and laid the foundation for the expansion of their potential applications. The results of this research work were applied in filling materials for negative pressure wound therapy system. For some specific medical applications in wound management, the pore size of filling material was required to in the range of 200-500 micrometers. This pore size will facilitate the transmission liquids. By using our approach, the size of voids of new designed composite structures was determined by the cell size of the base material which was available and easy to manufacture such as conventional black foams in this study, while the NLC behaviour was dominated by the reinforcement component. The developed composite structures are under further assessment aiming to deploy the next generation of superior negative pressure wound therapy system for open abdomen wound closure. Finally, the conclusions of this thesis were summarized in chapter 5.
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