Designing complex re-entrant honeycombs with optimal auxeticity

• Complex multi-node re-entrant honeycomb metastructures offer a large design space. • Poisson’s ratio is optimized for small deformation with an optimization framework. • Optimization framework can be extended for design of 3D re-entrant metastructures. • Maximum strain maintaining desired auxeticity under large deformation is optimized. Due to their distinctive mechanical properties, re-entrant honeycomb structures have attracted significant attention across various engineering fields, including aerospace applications. In this work, we propose a complex multi-node re-entrant honeycomb metastructure along with a corresponding design methodology. The mechanical behavior of these metastructures is accurately characterized using the stiffness matrix method. A genetic algorithm is employed to optimize the coordinates of internal nodes, minimizing the Poisson’s ratio under small deformations within a large design space. The results demonstrate that the proposed theoretical approach and optimization framework achieve high accuracy. Moreover, the optimized metastructure exhibits a significantly more negative Poisson’s ratio than conventional designs. The framework is also extensible to 3D structures, with the 3D stiffness matrix method enabling the successful optimization of 3D multi-node re-entrant metastructures. Additionally, by integrating the Updated Lagrangian method with the genetic algorithm, the desired Poisson’s ratio can be maintained under large strains.