* 3 D Soft Metamaterials with Negative Poisson ’ s Ratio A TIO

A IO N When materials are uniaxially compressed, they typically expand in directions orthogonal to the applied load. Here, we exploit buckling to design a new class of three dimensional metamaterials with negative Poisson's ratio that contract in the transverse direction under compressive loading regimes. These proposed metamaterials consist of an array of patterned elastomeric spherical shells, which due to a mechanical instability, undergo a signifi cant isotropic volume reduction when deformed. The large geometric non-linearities introduced in the system by buckling are exploited to achieve a negative Poisson's ratio and retain this unusual property over a wide range of applied deformations. Here, we identify a library of auxetic building blocks and defi ne procedures to guide their selection and assembly. The auxetic properties of these materials are demonstrated both through experimental and fi nite element simulation approaches and exhibit excellent qualitative and quantitative agreement. As a result of this unusual behavior, these proposed metamaterials could be useful for the design of protective and energy absorbing materials, effi cient membrane fi lters with variable permeability, and acoustic dampeners. Metamaterials are rationally designed artifi cial materials which gain their properties from structure rather than composition. Since it was fi rst shown that microstructures built from non-magnetic conducting sheets can exhibit effective magnetic permeability, [ 1 ] the metamaterial concept has been quickly extended to photonic, [ 2 ] acoustic [ 3 ] and mechanical, [ 4 ] systems, leading to the design of a variety of materials with properties not previously thought possible. The Poisson's ratio defi nes the ratio between the transverse and axial strain. [ 5 ] Materials that are uniaxially compressed