Designing Hierarchical Honeycombs to Mimic the Mechanical Behaviour of Composites

Honeycombs are used ubiquitously in engineering applications as they have excellent out-of-plane strength and stiffness properties with respect to weight. This paper considers the properties of honeycombs in the in-plane direction, a direction that is significantly weaker and less stiff than the out-of-plane direction. We assess how judiciously locating structural hierarchy within a honeycomb array can be a geometric design principle with direct consequences on the mechanical behaviour of the honeycomb. Here, we use finite element methods to design reinforced honeycomb mechanical metamaterials that mimic the mechanical behaviour of unidirectional fibre reinforced composites. We specifically incorporate structural hierarchy within hollow honeycomb cells to create mechanical metamaterial pseudo-composites, where the hierarchical parts are pseudo-fibres, and the hollow parts are the pseudo-matrix. We find that pseudo-fibre contribution coefficients are higher than the fibre contribution coefficient of carbon fibre reinforced plastics (CFRP). We also find that the elastic modulus of unidirectional pseudo-composites can be predicted using the (Voigt model) rule of mixtures with a good level of accuracy.