Mechanical behaviors of a novel auxetic honeycomb characterized by re-entrant combined-wall hierarchical substructures

The current focus of the metamaterials is to further improve their performance by the unit cell innovation, while for the auxetic metamaterials, the compromise between the mechanical properties and auxetic effect still needs more efforts. Given this issue, here we developed a novel auxetic honeycomb, named re-entrant combined-wall (RCW) honeycomb, by introducing four hierarchical substructures to the RE cell. Analytical expressions were derived and used to study the in-plane elastic constants of the RCW honeycomb, which were well confirmed by the established finite element model. Further, we investigated its crushing behaviors under large deformation by the explicit numerical method, and the quasi-static crushing experiments were also carried out by the 3D-printed specimens. Results show that the properties of the proposed RCW honeycomb have a high degree of orthogonality and tunability. Compared with the traditional RE honeycomb, the Young's modulus of the RCW honeycomb in the y direction increases by more than 120%, and the Poisson's ratio decreases by about 43%. Besides, behaviors of the cell wall contact induced by the adding substructure can lead to an interesting stress enhancement phenomenon under large deformation, which significantly increases its crushing strength, up to 140%, compared with the RE honeycomb. Therefore, the results in this work effectively demonstrate the improved mechanical properties and auxetic performance of the proposed RCW honeycomb. Besides, the adopted design strategy of hierarchical substructure also exhibits great potential for developing novel and excellent auxetic mechanical metamaterials.