A mathematically defined 3D auxetic metamaterial with tunable mechanical and conduction properties

An auxetic metamaterial is a type of mechanical metamaterial that has negative Poisson's ratio. Most auxetic metamaterials are truss-based or originate from Boolean operations of simple geometries. Herein, we introduce a new 3D auxetic metamaterial that is mathematically generated from an implicit expression. Further, this metamaterial is fabricated by 3D printing using a flexible material, which allows it to recover from large deformations. The buckling-induced auxetic behavior of the metamaterial was evaluated via compression tests and finite element analyses. A nickel layer was then plated on the surface to enhance its stiffness, strength, and conductivity without loss of auxeticity and resilience. The integration of 3D printing and electroless plating thus enables accurate control over the mechanical and conduction properties of the auxetic metamaterial; these properties are presented as contour maps for guidance in functional applications.