Design and Microscale Fabrication of Negative Poisson’s Ratio Lattice Structure Based on Multi-Scale Topology Optimization

Abstract

The current design of negative Poisson’s ratio lattice structures is mainly forward-looking and predominantly dependent on several known deformation patterns. To automate the generation of structures with programmable Poisson’s ratio, the study utilized the energy homogenization method and the Solid Isotropic Material with Penalization (SIMP) method to establish an optimization model for negative Poisson’s ratio. By proposing a relaxed objective function and eliminating damping in the Optimality Criteria (OC) method, the study achieves the automatic evolution of negative Poisson’s ratio programmable lattice unit cells, with the lowest Poisson’s ratio achieving −0.5367, and an equivalent elastic matrix is derived. The iterative process’s efficiency is comparable to that of commercial software, with a maximum iteration time of 300 s, enabling the prompt identification of fundamental configurations. To validate the method’s effectiveness, finite element analysis was performed on four tubular structures, revealing evident tension–compression deformation patterns. Moreover, the microscale selective laser melting was used to successfully prepare multiple sets of tubular samples made from 316L stainless steel, each with a height of 5 mm. Quasi-static compression experiments showed negative Poisson’s ratio effects and buckling forms that align with finite element analysis results, providing valuable insights for industry applications.