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Simple closedform results for all the independent elastic constants of macro, micro and nanosized firstorder regular honeycombs
with square and equilateral triangular cells and for the selfsimilar hierarchical honeycombs were obtained. It is found that, if the cell wall
thickness of the firstorder honeycomb is at the micrometer scale, the elastic properties of a hierarchical honeycomb are size dependent,
owing to the strain gradient effects. Further, if the firstorder cell wall thickness is at the nanometer scale, the elastic properties of a hierarchical
honeycomb are not only size dependent owing to the effects of surface elasticity and initial stresses, but are also tunable. In addition,
the cell size and volume of hierarchical nanostructured cellular materials can be varied, and hierarchical nanostructured cellular
materials could also possibly be controlled to collapse.
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