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• The proposed auxetic honeycomb possesses more excellent auxetic behavior and specific energy absorption than the conventional honeycomb. • The interaction between the structural parameters is analyzed. • The multi-objective optimization of the enhanced auxetic honeycomb (EAH) was investigated. • The theoretical model and Box-Behnken Design model were used to predict the mechanical properties of EAH. In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures. [ABSTRACT FROM AUTHOR]

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. Image 1 • Analytical predictions of the NPR effect under large deformation exhibits a good agreement with the numerical results. • A special deformation mechanism and stress-strain behavior are illustrated by the experiments and numerical simulations. • The negative Poisson's ratio (NPR) of the honeycombs varies differently with strain at different stages. • Variation of cell-geometry parameters greatly influence the NPR effect of the honeycombs. • More evident NPR effect is exhibited when the honeycomb gradually develops into the conventional re-entrant honeycomb. [ABSTRACT FROM AUTHOR]

In order to comprehensively understand the dynamic response of auxetic honeycombs, theoretical analysis are conducted to predict the NPR effect and the crushing stress of the re-entrant hexagonal honeycomb. The honeycomb’s crushing stress is a function of the cell’s geometric parameters, crushing velocity and the mechanical property of the cell-wall material. Results show that the crushing stress enhances with the increasing crushing velocity. A dynamic sensitivity index is employed to quantitatively evaluate this enhancement. It is shown that small cell-wall angle, low relative density or high cell-wall length ratio of the honeycomb attribute high velocity-sensitivity to the crushing stress. The Poisson’s ratio of the re-entrant honeycomb is also expressed as a function of the cell’s geometric parameters. It is revealed that the NPR effect enhances with the increasing cell-wall angle and the decreasing cell-wall length ratio. All the theoretical predictions are verified by numerical simulations. Besides, an interesting phenomenon is noticed that the crushing velocity has significant influence on the honeycomb’s NPR effect at the early stage of crushing. However, this influence almost vanishes when the overall strain is larger than about 0.2. This present work is supposed to shed light on the design of the auxetic honeycomb. [ABSTRACT FROM AUTHOR]