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Metastructures are extensively used in aerospace engineering. In the present work, a high-strength structure was designed based on a reentrant hexagonal honeycomb (RHH) by topology optimization. To generate a negative Poisson's ratio (NPR) effect, topologically optimized cells were alternately arranged with RHH cells to obtain a hybrid hexagonal honeycomb (HHH). In comparison with other NPR structures, this structure had superior energy absorption characteristics. In addition, the mechanical properties and deformation behavior of this structure were analyzed. Finally, single, double, and triple functional gradients were introduced into the HHH. It was found that the introduction of functional gradients improved the energy absorption capacity of the structure, and that the energy absorption capacity increased with the increase in the number of functional gradients. [ABSTRACT FROM AUTHOR]