The effects of hierarchy on the in-plane elastic properties of honeycombs

Introducing hierarchy into structures has been credited with improving elastic properties and damage tolerance. Specifically, adding hierarchical sub-structures to honeycombs, which themselves have good-density specific elastic and energy-absorbing properties, has been proposed in the literature. An investigation of the elastic properties and structural hierarchy in honeycombs was undertaken, exploring the effects of adding hierarchy into a range of honeycombs, with hexagonal, triangular or square geometry super and sub-structure cells, via simulation using finite elements. Key parameters describing these geometries included the relative lengths of the sub- and super-structures, the fraction of mass shared between the sub- and super-structures, the co-ordination number of the honeycomb cells, the form and extent of functional grading, and the Poisson’s ratio of the sub-structure. The introduction of a hierarchical sub-structure into a honeycomb, in most cases, has a deleterious effect upon the in-plane density specific elastic modulus, typically a reduction of 40 to 50% vs a conventional non-hierarchical version. More complex sub-structures, e.g. graded density, can recover values of density specific elastic modulus. With careful design of functionally graded unit cells it is possible to exceed, by up to 75%, the density specific modulus of conventional versions. A negative Poisson’s ratio sub-structure also engenders substantial increases to the density modulus versus conventional honeycombs.