Auxetic metamaterials exhibit certain extraordinary properties such as negative Poisson’s ratios, which means lateral compression and expansion under compressive and tensile loads respectively. This abnormal deformation of these materials eventually leads to the enhancement of some mechanical properties in the form of enhanced shear resistance, indentation resistance, fracture resistances etc., and qualify them to be used in numerous applications areas, be it medical, such as stents with controlled deformation or industrial, for example, as crash-worthy helmets. Over the years, numerous structural auxetic forms evolved, falling into a general classification of three specific groups, re-entrant, chiral, and rotating units. While analytical models dominated these endeavours and went far ahead in claiming extremely auxetic nature with specific structural models, the main bottle neck had always been the physical implementation of the structures and the experimental verification of the analytical claims.

The volumetric compression methods in single and multi-stage heating and compression, the thermoforming route, melt-spinning techniques, chemical and mechanical compression method and the CO2 gas assisted compression techniques evolved in the past, but for most part these were restricted to developing simple polymeric or metallic auxetic foams. With the recent developments in additive manufacturing, the freedom to produce more complex auxetic shapes is enhanced significantly. However, the overall development considering metallic materials and selective laser melting technique was still limited. Also the focus was mainly limited to geometrically optimising the structures for better auxeticity of the re-entrant structures. The other structural forms such as square grid and chiral forms did not get much attention. The critical aspects of structural analyses such as stress concentration effects were also neglected largely. The research reported in this thesis is designed to address these issues and fill the gaps.

The square-grid auxetic structure is used initially as the basis for developing the experimental and numerical schemes and their integration to find answers to the research questions raised. Numerical simulations based on the finite element methods and the compression tests conducted on laser melted structures are used to correlate the data generated and fine-tune and bring the numerical schemes close to the reality. The final numerical simulation schemes are then used to optimise the square-grid structures into non-square-grid structures, targeting much higher auxetic responses, which led to the invention of a non-square grid form with Poisson’s ratio as high as -7. Further, the numerical schemes established are also used to evaluate the stress concentration aspects which eventually led to the design of a new chiral type S-shaped structural form. The new S-shaped structure is auxetic to a reasonable extent, while also allowing to avoid the stress concentration issues but at the cost of reduced mechanical properties against the re-entrant structural model. Further, a few hybrid structures were also proposed and evaluated which outperformed the parent S-shaped models, by means of acquiring the best qualities of both the unit cells used to form the structures. Overall, the fabrication of metallic auxetic structures by selective laser melting together with the optimisation by the finite element schemes proved to be effective in developing truly auxetic structures with controlled responses and performance attributes and ready for real world applications.