Modeling of uniaxial compression in a 3D periodic re-entrant lattice structure

In this study, the behavior of a parametric 3D re-entrant dodecahedron lattice structure with negative Poisson’s ratio was studied. Four geometrical configurations for the re-entrant dodecahedron were designed, and the relationship between the mechanical properties and the design parameters was determined through beam theory. Samples were fabricated successfully via electron beam melting. Compressive tests as well as finite element analysis (FEA) were performed, and the results were compared with theoretical predictions. The modeling yielded explicit analytical equations of various mechanical properties including Poisson’s ratios, modulus and strength, and the compressive strength and the modulus from the prediction match well with the experiments, as well as the FEA results. The methodology used by this study also demonstrated a feasible approach to design 3D auxetic cellular structure for various applications.