A novel three-dimensional auxetic lattice meta-material with enhanced stiffness

This paper proposes a three-dimensional (3D) lattice meta-material made by extending the existing two-dimensional enhanced auxetic model to a 3D one. With narrow ribs embedded into every cell of the typical 3D re-entrant honeycomb (TRH), the new structure can also be considered as an enhanced design of the TRH. A combination of theoretical and numerical analysis is carried out to gain a deeper understanding of the elastic behavior of the new 3D structure and its dependence on the geometric parameters. The new structure is proved analytically and numerically to exhibit a negative Poisson's ratio, while its Young's modulus is significantly improved compared to that of the TRH. It is remarkable that the Young's modulus of the new structure increases linearly with the relative density while an approximate square relation is found between that of the THR and the relative density, which reveals that the dominated deformation model of the micro-structures has been changed by the embedded ribs from bending to stretching. The present layout may be promising for some special applications due to its superior performance and may provide a new concept for the optimization design of 3D auxetic materials, whose stiffness is relatively low.