Numerical and theoretical analysis of crushing strength of 3D re-entrant honeycomb

Auxetic structures with negative Poisson's ratio (NPR) have been widely studied because of their great potentials in energy absorption. In order to further understand the 3D auxetic structures, especially the 3D re-entrant honeycombs, the crushing response of metallic 3D re-entrant honeycomb (3D-RH) is theoretically studied in this paper. First, the finite element (FE) model of the 3D-RH was built and validated. The numerical simulation results show that the 3D-RH exhibits different deformation modes under low-and high-speed crushing. Secondly, a set of numerical simulations was used to determine the critical velocity that distinguishes the two deformation modes. Based on the predicted deformation profile, the crushing strength of 3D-RH under low-and high-speed crushing was derived in the form of theoretical equations. The relative errors between the theoretical and numerical results are less than 10%. Thirdly, the structural parameters were studied to reveal their effects on the crushing strength of 3D-RH. The results showed that the oblique wall length and cell wall thickness have significant effects on the crushing strength, while the cross length and cell wall width have little effect on the crushing strength. In addition, the re-entrant angle has no obvious effect on the low-speed crushing strength, but has a significant effect on the high-speed crushing strength. Finally, considering the rotational symmetry of the 3D-RH unit, the 3D-RH-nRP unit was found, which is a new type of 3D re-entrant unit with multiple re-entrant parts. The corresponding equations of crushing strength were derived. The FE results showed that the equations can well estimate the crushing strength of 3D-RH-nRP structures.