Elastic Properties of an Additive Manufactured Three-Dimensional Vertex-Based Hierarchical Re-Entrant Structure

This work proposes a new auxetic lattice based on replacing the vertexes of traditional three-dimensional re-entrant structural with self-similar configurations. Derived by Castigliano's second theorem, a theoretical model is built to predict its elastic mechanical properties, including the homogenized Young’s modulus and Poisson’s ratio in all three principal directions. The overlapped nodes of struts are considered in the theoretical model due to their excessive strut thickness. The analytical results exhibit good agreement with the numerical and experimental results. The effects of the geometric parameters, internal force species, and hierarchical magnitude on the elastic property are carefully studied. The findings suggest that the axial internal force in the new structure inhibits its auxetic effects in the three principal directions. Compared with the traditional three-dimensional re-entrant lattice with equal relative density, the vertex-based hierarchical one exhibits more comprehensive designability of auxetic effect and enables higher Young’s modulus with specific geometrical parameters. The findings in this study contribute to the metamaterial advancement and provide an option for engineering applications requiring programmable and controllable elastic properties.