Mechanical behaviors of hierarchical cellular structures with negative Poisson's ratio

An investigation of the mechanical behaviors on hierarchical re-entrant honeycomb structures was undertaken using finite element method. The hierarchical structure with a hierarchy order n (n >= 1) was constructed by replacing each vertex of a re-entrant hexagonal structure of hierarchy order n - 1 with a smaller re-entrant hexagon with identical geometry aspect ratio. The Poisson's ratio and energy absorption capacity of re-entrant structures of different hierarchy orders were studied under various compression velocities. The minimum Poisson's ratios of the first-order (n = 1) and second-order (n = 2) hierarchical re-entrant structures were - 1.581 and - 1.823, respectively; they were 32.9 and 53.2% lower than that of a zeroth-order hierarchical structure (i.e., conventional re-entrant hexagon). The second-order hierarchical structure exhibited the highest rate of increase in energy absorption capacity with an increasing compression velocity. The plateau stresses of the first- and second-order hierarchical structures were lower than that of the zeroth-order hierarchical structure; however, the second-order hierarchical structure exhibited the highest energy absorption capacity at high compression velocity rate (v > 40 m/s). The energy absorption capacities of the first- and second-order hierarchical structures proposed in the present study are 1.5 and 1.8 times, respectively, higher than those of the hierarchical re-entrant structures proposed in our previous work (Li et al. in Smart Mater Struct 26:025014, 2017).