Hierarchical honeycomb auxetic metamaterials

Most conventional materials expand in transverse directions when they are compressed uniaxially resulting in the familiar positive Poisson's ratio. Here we develop a new class of two dimensional (2D) metamaterials with negative Poisson's ratio that contract in transverse directions under uniaxial compressive loads leading to auxeticity. This is achieved through mechanical instabilities (i.e., buckling) introduced by structural hierarchy and retained over a wide range of applied compression. This unusual behavior is demonstrated experimentally and analyzed computationally. The work provides new insights into the role of structural organization and hierarchy in designing 2D auxetic metamaterials, and new opportunities for developing energy absorbing materials, tunable membrane filters, and acoustic dampeners.