Poisson's Ratio Material Distributions

The Poisson’s ratio of materials describes the ratio of the transverse to axial strain. While most materials exhibit non-negative Poisson ratio, here we focus on the topological properties of negative ratio materials also known as auxetic constructs. Digital modelling and physical fabrication are employed to generate and test experimental auxetic configurations. The first set of studies employ 2D space-filling tessellations integrating both negative and positive Poisson ratio cells. The tessellations are designed through binary state transitions and gradual morphing transitions. A second set of studies explores the topological optimization of a single negative Poisson cell configuration following the logic that a cell constitutes the building block of auxetic materials. The third set of studies focuses on the translation of heterogeneous Poisson ratio 2D tessellations into 3D constructs. Here, two methods of fabrication are explored: lamination method and cellular grading. The precision of the cellular grading method renders it particularly suitable for multi-material 3D printing fabrication which is theoretically studied and proposed. Space-filling heterogeneous tessellation studies are applied to architectural and product design proposals. These proposals exhibit properties that could serve to design and develop further research on real-world applications.