Curved inserts in auxetic honeycomb for property enhancement and design flexibility

Imperfect situation, like the non-uniform cross-section or non-straight profile of cell walls, can in certain case be a positive contributor for properties of cellular solids. However, auxetic cellular structures with imperfect profiles are rarely reported in the literature. Based on the re-entrant hexagonal honeycomb (RHH), this paper developed two new types of honeycombs with curved inserts and focused on the issue that how microscopic curved inserts influence the auxetic structure's macroscopic mechanical properties? Theoretical models for the in-plane equivalent elastic moduli of the two types of new honeycombs, including the Young's modulus, Poisson's ratio and shear modulus, were first established, and then verified by numerical simulations. The results showed that the two types of new honeycombs possess the same ability to achieve auxeticity, in the meantime, exhibit improved Young's modulus and shear modulus compared to the RHH. Furthermore, the new honeycombs demonstrate more flexibility in design as the curved inserts can offer more geometric parameters for tailoring their macroscopic mechanical properties. The study also showed that the curved inserts played a key role in determining the dominated deformation mode of the new honeycombs, and a special dominated deformation mode intermediate between pure bending and stretching was found in these honeycombs. This work would provide a useful guide for the development and optimization of auxetic materials.