Design of planar isotropic negative Poisson’s ratio structures

Most of the auxetic materials that have been characterized experimentally or studied analytically are anisotropic and this limits their possible applications, as they need to be carefully oriented during operation. Here, through a combined numerical and experimental approach, we demonstrate that 2D auxetic materials with isotropic response can be easily realized by perforating a sheet with elongated cuts arranged to form a periodic pattern with either six-fold or three-fold symmetry. Moreover, we also show that the auxetic behavior can be easily tuned by varying the length of the cuts and that it is retained even under large levels of applied deformation beyond the limit of small strains. This novel, simple and scalable design can serve as an important guideline for designing and fabricating isotropic auxetic materials that can have a significant impact on a wide range of applications.