Shape Morphing of Re-Entrant Honeycomb Metamaterials for Linear Auxetic Behaviors

A re-entrant honeycomb structure stands out as one of the most prevalent auxetic metamaterials, characterized by its negative Poisson's ratio. While re-entrant auxetic structures are capable of achieving tunable Poisson's ratios, they tend to vary with the magnitude of applied strain, thereby exhibiting nonlinear auxetic behaviors. This study proposes a novel re-entrant structure aimed at achieving linear auxetic behavior by mathematically modifying the shape of a re-entrant cell. To achieve this objective, a sigmoid-based shape morphing function is introduced to modify the morphology of the hinge connections within the re-entrant honeycomb cell. The deformation behavior of the shape-morphed re-entrant cell is investigated using finite element analysis (FEA), with variations in the morphing parameter. Two FEA models, namely the unconstrained and constrained models, are developed for fundamental analysis of cell deformation and experimental validation, respectively. Compared to the pure re-entrant honeycomb structure, the proposed shape morphing reduces the relative variation of Poisson's ratio by 70%, while maintaining its magnitude higher than 1.0. This achievement of linear auxetics with a high Poisson's ratio has the potential to broaden the applications of the proposed auxetic structures to various functional components, including sensors with high linear sensitivity and soft actuators with tunable deformation characteristics.