Deformation behavior of re-entrant auxetic metamaterials considering shape transformation effects

A re-entrant hexagonal structure is the most popularly-used auxetic metamaterial providing unique deformation behavior with a negative Poisson’s ratio. In the re-entrant auxetic structure, the Poisson’s ratio varies depending on the design of the re-entrant shape and the order of deformation. In this study, the deformation behavior of re-entrant auxetic structures was investigated through experimental and numerical analyses, with a variation of the reentrant angle. The experimental results showed that the Poisson’s ratio increased as the reentrant angle decreased, and the auxetic property was maintained only while a re-entrant cell remained in a concave shape. Finite element analyses (FEAs) were also conducted to investigate the deformation behavior of the re-entrant structures, using ID-beam and 2D-continuum elements. Compared to the experimental findings, the 2D-FEA showed similar results both in the concave and convex deformation regimes whereas the 1D-FEA showed a reliable prediction only in the concave regime. Additionally, consideration of the cell curvature in the 2D-FEA provided better simulation accuracy by appropriately describing the transformation from the concave to convex regimes. The relevant Poisson’s ratio data were then statistically analyzed to obtain a bilinear regression equation as a function of the axial strain and re-entrant angle, which provides insights into the deformation behavior of re-entrant structures.