Multi-scale characterization of novel re-entrant circular auxetic honeycombs under quasi-static crushing

Auxetic honeycombs showing negative Poisson's ratio (NPR) effects have attracted extensive attentions due to their excellent mechanical properties, among which those with the innovative re-entrant circular (REC) unit cells have proven to present higher energy absorption capabilities than their equivalents with conventional re-entrant (RE) units, under quasi-static loading. In the current study, the quasi-static crushing strengths and energy absorption capabilities of the REC honeycombs with different geometric parameters are thoroughly investigated, through finite element (FE) based numerical simulations in combination with theoretical analyses. It was found that the crushing stress, the energy absorption characteristic and the auxeticity, i.e. the NPR value of the REC honeycomb can be tailored by adjusting the geometrical parameters of its unit cell to trigger specific deformation mechanisms in both meso (unit cell) and macro (total honeycomb) scales. Specifically, based on the cell wall interaction pattern, the REC unit cell configuration map can be divided into three distinctive regions, which are the penetration region, the interference region and the regular region, respectively. LS-DYNA based numerical simulations revealed three typical macro-scale deformation modes, i.e. the "X", the "I" and the "V" modes of the REC honeycomb in the three regions, corresponding to three mesoscale interaction patterns of the unit cell, including the "overlap", the "rectangle" and the "re-entrant" patterns. The quasi-static crushing stresses of the REC honeycombs with different geometric parameters were further compared and divided into four distinctive stages: the elastic stage, the plateau stage, the enhancement stage and the densification stage, respectively. Larger radius to height ratio and length to height ratio were found to result in larger plateau strain and smaller plateau stress. Good agreements were achieved between the numerical and theoretical predictions of the plateau strain and plateau stress of the REC honeycombs. Finally, the quasi-static energy absorption capabilities and the NPR values of the REC honeycombs with different geometric parameters were revealed and discussed, to assist engineering applications of such materials.