Size-dependent and tunable elastic properties of hierarchical honeycombs with regular square and equilateral triangular cells

Simple closed-form results for all the independent elastic constants of macro-, micro- and nanosized first-order regular honeycombs with square and equilateral triangular cells and for the self-similar hierarchical honeycombs were obtained. It is found that, if the cell wall thickness of the first-order 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 first-order 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.