Design and Optimization of a Highly Anisotropic Auxetic Honeycomb Structure Inspired by Branching Morphology

Auxetic materials, a class of metamaterials characterized by a negative ratio, demonstrate unique mechanical behavior by expanding laterally when stretched and contracting laterally when compressed, which make them widely applicable in fields such as force sensors and protective impact devices. However, conventional auxetic materials often struggle to simultaneously achieve low density and strong anisotropy under standard parametric configurations, failing to meet the increasing demands for material performance in diverse applications. Inspired by the Y-shaped branching morphology of trees, a highly anisotropic auxetic honeycomb structure was proposed by combining re-entrant and chiral mechanisms in this study, and the auxetic performance of this structure was analyzed and optimized. Firstly, specimens of the honeycomb structure were fabricated using 3D printing technology. Quasi-static tensile tests and numerical simulations were conducted to validate the reliability of the numerical model against experimental results, and the influence of key parameters on structural performance was investigated. Secondly, five key geometric parameters of the structure were selected as design variables. A Kriging surrogate model for structural mass and Radial Basis Function Neural Network models for elastic modulus and Paasion’s ratio were established. The multi-objective genetic algorithm (NSGA-II) was employed to invoke these surrogate models for optimizing the auxetic performance, ultimately obtaining the optimal combination of structural parameters. Comparative simulations and experiments between the optimized configuration and the initial configuration demonstrated that under identical mass conditions, the optimized configuration exhibits superior auxetic performance. The maximum Passion’s ratio measured in quasi-static tensile tests was − 7.18, and the load-bearing capacity increased by 187.17% compared to the initial structure.