Mechanics of chiral, anti-chiral, and hierarchical honeycombs

The effects of two geometric refinement strategies widespread in natural structures, chirality and self-similar hierarchy, on mechanical response of two-dimensional honeycombs were studied systematically.;First, by employing the concepts of mechanics of materials, simple closed-form expressions were derived for the elastic moduli of several chiral, anti-chiral, and hierarchical honeycombs with hexagon and square based networks. The analytical results were validated using finite element analysis and experimental data available in the literature.;Next, a new class of hierarchical fractal-like honeycombs inspired by the topology of the "spiderweb" was introduced and investigated for its small and large deformation response through analytical modeling, detailed numerical simulations, and mechanical testing. For small deformations, the elastic moduli can be controlled by geometrical ratios in the hierarchical pattern, and the response can vary from bending to stretching dominated. These structures exhibit auxetic behavior at large deformations.;Next, we exploit mechanical instabilities and structural hierarchy to induce negative Poisson's ratio over a wide range of applied compressive strains in hierarchical structures which otherwise exhibit positive Poisson's ratio at small deformations. This unusual behavior is demonstrated experimentally and analyzed computationally.;Finally, we highlighted the effects of structural hierarchy and deformation on band structure and wave-propagation behavior of two-dimensional phononic crystals. We employed finite element analysis along with Bloch theorem to show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the band gaps and directionality of phononic crystals.