Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson’s ratio (PR) are called auxetics; they are characterized by expansion/contraction when tensioned/compressed. Given this counterintuitive behavior, they present very particular characteristics and mechanical behavior. Geometrical models have been developed to justify and artificially reproduce such materials’ auxetic behavior. The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters. It is shown that, even in the presence of protruding ribs, there may not be auxetic behavior, and this depends on the geometry of each reentrant structure. Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.