Parametric Optimization of a Two-Dimensional Double Arc Star-Shaped Auxetic Unit Cell Using a Hybrid SEO Algorithm

Auxetic structures are a class of mechanical metamaterials characterized by a negative Poisson’s ratio, which enables them to contract in the transverse direction when subjected to compression. Their mechanical response strongly depends on the geometry of the unit cell, making parametric optimization an important tool for improving their auxetic behavior. This study presents a procedure for optimizing the geometric parameters of a two-dimensional double arc star-shaped (2D-DASS) unit cell with the objective of minimizing its Poisson’s ratio while maintaining Young’s modulus, solid material volume, and total unit-cell volume within prescribed allowable deviations. The mechanical properties of the unit cell were determined analytically using Castigliano’s second theorem in conjunction with Euler–Bernoulli beam theory. The optimization procedure was applied to seven initial configurations, with the initial angle θ ranging from 35° to 65° in increments of 5°. Five geometric parameters, namely θ , l 1 , g , l 3 , and t , were considered as design variables. The results showed that the optimized angle reached 70° in all considered cases, while the constraints on Young’s modulus, solid material volume, and total unit-cell volume were satisfied within the prescribed allowable deviation of ± 0.5%. For initial angles of 35°, 40°, and 45°, the optimization procedure produced negative Poisson’s ratio values despite the positive values obtained from the initial analytical configurations. Furthermore, finite element analyses of structures composed of 3x3 unit cells demonstrated greater horizontal deformation in the optimized configurations under vertical compression. Comparisons between the analytical, optimization, and numerical results showed generally good agreement. The findings demonstrate the potential of the proposed procedure for improving the auxetic response of 2D-DASS unit cells while preserving their principal mechanical and geometric characteristics.