Journal of Materials Science

, Volume 53, Issue 14, pp 10209–10216 | Cite as

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

  • Jiahong Hou
  • Dong Li
  • Liang Dong


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).



This work is supported by “The Fundamental Research Funds for the Central Universities (N170504016).”

Compliance with ethical standards

Conflict of interest

Authors declare that no conflicting interests affected this research. Authors declare that no conflicting interests affected the objective presentation and description of results.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of SciencesNortheastern UniversityShenyangPeople’s Republic of China
  2. 2.Materials Science and EngineeringUniversity of VirginiaCharlottesvilleUSA

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