Negative Poisson's ratio effect of re-entrant anti-trichiral honeycombs under large deformation

Re-entrant anti-trichiral honeycomb is a typical auxetic material. The collapse process can be divided into three stages while its negative Poisson's ratio (NPR) effect under large deformation is still unclear. In the present paper, the NPR effects of re-entrant anti-trichiral honeycombs under large deformation are studied by numerical and theoretical method. Numerical results are verified by the experiments with respect to their deformation mechanism and stress-strain behavior. Theoretical formulas are derived to predict the NPR effect of the honeycomb under large deformation. The analytical predictions are in good agreement with the FEM results. It is revealed that the NPR effect of the honeycomb is magnified with the global strain in the second stage while is weaken in the third stage of the deformation process. The decrease of the ligament-ratio and the mean radius will result in more obvious NPR effect. Variation of cell-wall thickness doesn't have much impact on the Poisson's ratio in the second stage, while smaller cell-wall thickness will induce larger NPR in the third stage. The present work is supposed to shed light on the design and fabrication of re-entrant anti-trichiral honeycombs with desired Poisson's ratio.