Background: In-plane properties (e.g. stiffness, strength and energy absorption) of two-dimensional cellular structures are generally far inferior to their out-of-plane properties. Therefore, cellular structures with modified morphology and organization, such as hierarchical and functionally graded structures with varying wall thickness or cell size have been developed to improve the in-plane mechanical response. Among these, hierarchical cellular structures have exhibited a range of promising and/or novel properties such as elevated specific stiffness or strength, negative Poisson's ratio, multi-stage dynamic crushing, and enhanced energy absorption under quasi-static loading. Objective: A hierarchical family of honeycomb-based cellular structures is formed by systematic introduction of successively smaller hexagons wherever three cell walls meet. This process can be repeated to obtain hierarchical honeycombs of different order. The objective of the current work is to provide analytical and finite element investigation to quantify the mechanical response and collapse of these structures. Method: The analytical analysis is based on an upper bound estimate from competing plastic hinge mechanisms defined for a representative unit cell of structure. Numerical and analytical investigations are carried out to investigate the range of attainable mechanical properties for hierarchical honeycombs by varying the order of hierarchy and/or geometrical parameters at each order. Results: Hierarchical honeycombs of first and second order can be up to 2.0 and 3.5 times stiffer than regular honeycombs at the same density. Moreover, the results show that there is no upper limit on the maximum achievable specific stiffness by further increasing the order of hierarchy for low densities of hierarchical honeycombs. In terms of plastic strength, hierarchical honeycomb with one order of hierarchy exhibit a maximum improvement of approximately 60% in specific strength. Conclusions: The results show that a wide range of stiffness and strength ratios can be obtained for hierarchical honeycombs by varying geometrical parameters. The current work provides insight into the role of structural organization and hierarchy in regulating the mechanical behavior of materials, and new opportunities for development of novel materials and structures with desirable and perhaps actively tailorable properties.


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