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

• The analytical model for Poisson's ratio and effective Young's modulus of the vertex-based hierarchical re-entrant honeycomb structure was built by Timoshenko beam theory first time. • The overlapping effect has a great influence on the relative density of the vertex-based hierarchical re-entrant honeycomb structure, especially for a thick-wall one. • The effective Young's modulus and Poisson's ratio of vertex-based hierarchical re-entrant honeycomb structure can be tailored by adjusting geometrical parameters. • Embedding a re-entrant honeycomb at the vertex of the re-entrant honeycomb is effective for improving its effective Young's modulus. In this study, the mechanical properties of a vertex-based hierarchical re-entrant honeycomb structure ( H v ) 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 H v 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 H v with different geometric parameters was studied. The results indicate that the elastic properties of H v 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 ( H c )* were given. H c was compared with H v 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 H c is an effective way to enhance its elastic modulus and simultaneously maintain the negative Poisson's ratio in a wide range.