Mechanical properties of 2D hierarchical re-entrant cellular structures with Voronoi sub-structures

In this study, 2D hierarchical re-entrant cellular structures with Voronoi sub-structures were proposed. Their Poisson's ratios and energy absorption capacities (in-plane) were studied using the finite-element method. The effects of geometric parameters (Voronoi sub-structure irregularity, k , concave angle, θ , ratio of cell wall thickness to cell height, w ) on the lattice mechanical properties were investigated. Results showed that Poisson's ratio first decreased and then increased with an increasing θ when k is less than 0.5. A minimum Poisson's ratio of approximately −0.315 was achieved when k = 0.5 and θ = 60 ∘ . The 2D hierarchical re-entrant lattice structure exhibited a maximum energy absorption capacity when k = 0.2 and w = 1 / 3 , which is 3.9 times higher than that of the traditional re-entrant structure with solid ribs and of identical relative density.