A novel 3D bidirectional auxetic metamaterial with lantern-shape: Elasticity aspects and potential for load-bearing structure

Abstract

Lantern, also known as coloured-lantern making, is known for being an ancient traditional craft in China that can be dated back as early as West Han Dynasty. Inspired by the lantern, the lattice element is built by vertically rotating and duplicating the 2D units, then the 3D auxetic metamaterial is formed by connecting the 8 ligaments of the lattice element on two perpendicular planes. As the elastic behaviors associated with this metamaterial are still almost unknown to a large extent, in this study, an analysis has been conducted to investigate how the geometric parameters related to the lattice design influence its elasticity. For this reason, a novel 3D lantern-shaped honeycomb structure (LSH) has been proposed, the Castigliano's second theorem, energy principle, and Moore's theorem are utilized to solve its Young’s modulus and Poisson’s ratio in the three main directions. The theoretical results exhibit good agreement with the numerical and experimental results. The results showed that the elasticity of LSH structures can be programmed by adjusting a range of geometric parameters. In addition, LSH features a bidirectional zero Poisson effect and a good stress distribution during compression. It shows potential in terms of load-bearing to meet the requirement of lightweight and high stiffness. This structure shows good promise for applications in aerospace, construction and other fields.