Graded metastructure design for linearly auxetic deformation under tension: From 2D honeycombs to 3D truncated cones

Mechanical metamaterials exhibit special properties that cannot be realized in traditional materials. To enable a metamaterial with a sequential Poisson’s ratio and controllable expansion, a 2D-graded hybrid re-entrant honeycomb is designed in this work by coupling graded re-entrant unit cells with negative and positive Poisson’s ratios. The correlation between Poisson’s ratio and structural location under tension is studied by finite element analysis and experiments. The influence of microstructural parameters, including base angle, height ratio, and internal angle, on the relationship between the Poisson’s ratio and structural location is systematically analyzed. The theoretical analysis shows that the 2D-graded hybrid metastructures exhibit auxetic behavior with a linearly declined Poisson’s ratio along the tensile direction due to the introduction of a height ratio, resulting in gradual expansion and elongation. Furthermore, adjusting the variation of internal angles at a small height ratio can enhance the negative Poisson’s ratio of the 2D-graded hybrid re-entrant honeycomb. Finally, a 3D-graded conical metastructure exhibiting linear auxeticity is constructed based on the 2D-graded lattice. Considering their designed linearity of deformation under tension, the 2D- and 3D-graded metastructures can facilitate the design of conical profiles for an extendable rocket nozzle and other deployable devices.