Poisson Distribution

This research derives from the notion that in all of these cases, the unusual material behavior can be understood through the geometry of its microstructure and the geometrical adaptations resulting from applied loads. Stemming from the cellular architecture of materials, this study proposes 2D and 3D designs of cell configurations highlighting the impact that cell geometry and relative density can have on structure mechanical properties. Samples of material distributions are both fabricated and digitally simulated. Following a cumulative methodology, this investigation takes place in three stages: 2D topology studies, single cell compliant mechanism studies and 3D topology studies considering future manufacturing with multi-material additive processes. Each stage of physical and virtual prototyping and testing had specific objectives and procedures mentioned above and hence, revealed separate meaningful results. From the heterogeneous 2D topology study, it was possible to achieve a wide range of non-linear and non-uniform deformation at the global level (overall shape of the sample) using relatively simple and linear transformation of cells. On the other hand, the single cell compliant mechanism studies, which implements non-linearity into the cell itself, drastically expands the geometric diversity in addition to attaining more complex and systematic global deformation. Finally, the 3D topology studies presents a plethora of opportunities relating to design and engineering applications by verifying that the heterogeneous 2d topology can be successfully applied to 3D geometries. Through this research we have proposed two and three dimensional geometry to engineer and simulate customized classical and auxetic homogeneous and heterogeneous material distributions. Extension to further practical design applications is currently in progress.