A novel 3D re-entrant unit cell structure with negative Poisson's ratio and tunable stiffness

In this paper, a novel three-dimensional (3D) unit cell structure with butterfly-like perforations was designed, and negative Poisson's ratio and tunable stiffness were achieved in such a geometry. The Poisson's ratio and strain-stress relationship of structures with different geometric parameters were determined using the finite element method (FEM). Samples with identical geometric variables to those of finite element models were fabricated via 3D printing technique, and their Poisson's ratios and stress-strain relationships were experimentally determined and compared with the FEM results. Results showed that the proposed 3D cellular structures exhibit negative Poisson's ratios, and a minimal value of -0.7091 could be reached. The stress-strain curve of each structure exhibited three distinct stages (elastic response, rib buckling and self-contact), with different elastic moduli being observed at each stage, and demonstrated a tunable range of the compressive stiffness ratio between stages varying from 0.1866 to 1.4006(tunable stiffness), as determined by FEM analysis. Good agreement was found between the experimental results and FEM predictions. The design concept can be implemented and optimized for specific applications via geometric parameters manipulation.