Functional grading in hierarchical honeycombs: Density specific elastic performance

The introduction of hierarchy into structures has been credited with improving their elastic and other properties. Similarly, functional grading has been demonstrated to increase the damage tolerance of honeycomb structures, although with the penalty of reduced Young's modulus or increased density. The combination of both hierarchy and functional grading has not been reported for honeycomb structures, although it is known in natural materials. A parametric numerical modelling study has been made of the in-plane elastic properties of honeycombs and how they are affected by functional grading and hierarchy, and importantly to establish whether it is possible to avoid reductions in Young's modulus. A set of analytical models has been developed to describe functional grading and hierarchy in honeycombs, based upon beam mechanics and the transform section method. The conditions for transition of a hierarchical honeycomb in behaviour from that of a discrete structure to that of a continuum are established. Furthermore, conditions are established for which hierarchical honeycombs, uniform or functionally graded, can surpass in-plane Young's moduli of conventional honeycombs a by factor of up to 2, on an equal density basis.