Stiff, strong and auxetic; ultra-light hierarchical meta-materials in 2-d

Through a combination of analytic and computational work, we examine the effect of adding hierarchical substructures to an auxetic lattices. Scaling results are found for the stiffness and strength of these lattices which are confirmed through computational studies.
We present a novel methodology allowing for the computation analysis of hierarchical structures where direct simulation would prove intractable. We show that through hierarchy one can create auxetic meta-materials of unprecedented stiffness. Furthermore, the strength of these ultralight meta-materials is enhanced by the introduction of hierarchy. Auxetic materials have a broad range of potential applications, and thus the creation of meta-materials with such stiffness and strength is undoubtedly of practical importance.