Numerical analysis on mechanical behaviors of hierarchical cellular structures with negative Poisson's ratio

Two-dimensional hierarchical re-entrant honeycomb structures were designed and the mechanical behaviors of the structures were studied using a finite element method. Hierarchical re-entrant structure of order n (n >= 1) was constructed by replacing each vertex of a lower order (n - 1) hierarchical re-entrant structure with a smaller re-entrant hexagon with identical strut aspect ratio. The Poisson's ratio and energy absorption capacity of re-entrant structures of different hierarchical orders were studied under different compression velocities. The results showed that the Poisson's ratio of the first and second order hierarchical structures can reach -1.36 and -1.33 with appropriate aspect ratio, 13.8% and 12.1% lower than that of the zeroth order hierarchical structure. The energy absorption capacity of the three models increased with an increasing compression velocity; 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 slightly 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 (60 m s(-1)).