Dimpled elastic sheets: a new class of non-porous negative Poisson’s ratio materials

The Poisson’s ratio, ν, defines the ratio between the lateral and axial strains in a material under uniaxial loading. Theoretically, in linear isotropic materials, the Poisson’s ratio can range between −1 and 1/2. A material with ν = 1/2 shears easily and resists volumetric deformations due to its vanishing shear (G = 0) and infinite bulk (K → ∞) modulus. Conversely, a material with ν = −1 resists shear (G → ∞), but easily undergoes volumetric deformations (K = 0). Outside this range, either the shear or bulk modulus of the material is negative, which is impossible due to thermodynamic stability1. Although the traditional belief is that the Poisson’s ratio of elastic materials must be positive (so that they shrink/expand laterally when stretched/compressed axially), since 1980s many 2D and 3D structures and materials with negative Poisson’s ratio have been reported2,3,4,5,6. Auxetic behavior was first realized in 2D re-entrant honeycomb structures that unfold and expand laterally when uniaxially stretched7,8. The same concept was later exploited by Lakes to design and fabricate the first 3D polymeric foam with isotropic auxetic behavior9. Subsequently, a number of geometries were proposed to achieve negative Poisson’s ratio through rotation of the stiffer components in the microstructure. These include chiral honeycombs10,11, networks of rigid rotating units12,13,14,15, and elastomeric porous structures in which instabilities are exploited to trigger the rotation of stiff domains16,17,18. Finally, negative Poisson’s ratio was realized in non-porous systems either by embedding an auxetic network within a compliant matrix19,20 or by using angle-ply laminates21,22,23,24,25,26. Till now, the majority of materials designed to have negative Poisson’s ratio are porous and this significantly limits the potential applications of auxetic materials. Although low porosity auxetic sheets comprising an array of elongated holes have been recently designed15, porosity is still crucial for inducing negative Poisson’s ratio in these systems and, hence, their auxetic response disappears if made non-porous. Auxetic composites can overcome this limitation due to their non-porous structure. However, since their response highly depends on the contrast between the material properties of their different phases, a limited set of engineering materials and manufacturing techniques can be used for their fabrication, making them unsuitable for many industrial applications. Here, we introduce a new class of auxetic materials that are non-porous and are easily fabricated out of any elastic sheet using conventional manufacturing techniques.