Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs

In this paper, we analytically studied the in-plane elastic and transport properties of a peculiar hexagonal honeycomb, i.e., the multifunctional hierarchical honeycomb (MHH). The MHH structure was developed by replacing the solid cell walls of the original regular hexagonal honeycomb (ORHH) with three kinds of equal-mass isotropic honeycomb sub-structures possessing hexagonal, triangular and Kagome lattices. Formulas to calculate the effective in-plane elastic properties and conductivities of the MHH structure at all densities were developed. Results show that the elastic properties of the MHH structure with the hexagonal sub-structure were weakly improved in contrast to those of the ORHH. However, the triangular and Kagome sub-structures result in substantial improvements by one or even three orders of magnitude on Young's and shear moduli of the MHH structure, depending on the cell-wall thickness-to-length ratio of the ORHH. The present theory could be used in designing new tailorable hierarchical honeycomb structures for multifunctional applications.