Negative Poisson's ratio and effective Young's modulus of a vertex-based hierarchical re-entrant honeycomb structure

Abstract In this study, the mechanical properties of a vertex-based hierarchical re-entrant honeycomb structure (Hv) were investigated. Firstly, the overlapping effect of struts was considered in the calculation of the relative density. The results indicate that the overlapping has a great influence on the relative density, especially for a thick-walled structure. Secondly, the theoretical model for evaluating Young's modulus and Poisson's ratio of Hv was implemented based on Castigliano's second theorem and Timoshenko beam theory. It shows a good coincidence between the results of the finite element and theoretical models. Thirdly, based on the theoretical model, the variation of the mechanical properties of Hv with different geometric parameters was studied. The results indicate that the elastic properties of Hv can be designed by appropriately adjusting geometrical parameters. Additionally, the expressions for effective Young's modulus and Poisson's ratio of the conventional re-entrant honeycomb (Hc)* were given. Hc was compared with Hv in terms of the elastic properties by applying the same theory and calculation process. The resultant comparisons suggest that embedding a re-entrant honeycomb at the vertex of Hc is an effective way to enhance its elastic modulus and simultaneously maintain the negative Poisson's ratio in a wide range.