Qualitative analysis and conceptual design of planar metamaterials with negative Poisson's ratio

This paper presents a new mechanics-based framework for the qualitative analysis and conceptual design of mechanical metamaterials, and specifically materials exhibiting auxetic behavior. The methodology is inspired by recent advances in the insightful synthesis of compliant mechanisms by visualizing a kinetostatic field of forces that flow through the mechanism geometry. The framework relates load flow in the members of the microstructure to the global material properties, thereby enabling a novel synthesis technique for auxetic microstructures. This understanding is used to qualitatively classify auxetic materials into two classes, namely, high-shear and low-shear microstructures. The ability to achieve additional attributes such as isotropy is shown to be related to the qualitative class that the microstructure belongs.