Tunable in-plane mechanical properties of the novel re-entrant auxetic structure with sinusoidal inclusion

This study proposes a novel orthogonally sinusoidal embedded auxetic architecture based on the cross-reinforced re-entrant hexagonal honeycomb, which utilizes a pre-buckling design methodology. An energy-based analytical model is developed to derive closed-form expressions for in-plane elastic properties, explicitly correlating them with sinusoidal amplitude. Under quasi-static compression, experiments and simulations reveal the tunable in-plane compressive performance and stable deformation of the auxetic structures, with good agreement. The novel auxetic topology achieves over 300 % increase in specific energy absorption relative to the conventional re-entrant configuration. The inherent compliance of sinusoidal inclusions enables the novel auxetic structures to sustain a stabilized stress plateau during initial compression phases, effectively eliminating the stress drop observed in the cross-reinforced counterpart. These metamaterials demonstrate superior deformation stability and pronounced dynamic negative Poisson's ratio effect. The in-plane compressive mechanical properties differ significantly between the two principal directions, with the y -direction exhibiting superior load-bearing capacity and energy absorption capability. Moreover, the impact simulations indicate that these engineered auxetic honeycombs exhibit significant applicability in impact mitigation systems, given their outstanding energy dissipation capacity.