Ali Behbahani - Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran
Amir Nourani - Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran
Sharif Shabani - Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran

Auxetic metamaterials have a negative Poisson's ratio (NRP), and this irregularity makes them suitable for numerous engineering applications, such as enhancement in indentation resistance and energy absorption. The Poisson's ratio of re-entrant auxetic structures is highly strain-dependent, and it can remain negative exclusively over a specific strain range. In re-entrant hexagonal cells, the Poisson's ratio increases with strain, surpasses zero, and becomes positive, which exterminates the auxetic characteristics of the structure. This study proposes a parametric analysis based on the structure geometry and performs a multi-objective optimization based on the auxeticity range and Poisson's ratio. A design of experiment (DOE) was carried out using the Taguchi method to find an empirical relation between Poisson's ratio and strain. The finite element method (FEM) was deployed to investigate the mechanical response of re-entrant structures to tensile loading. Using a statistical analysis, geometrical parameters were ranked based on their influence on Poisson's ratio. The empirical relation between the geometrical parameters, Poisson's ratio, and the auxeticity range was obtained to achieve the best geometrical configuration of the re-entrant structure using a genetic algorithm optimization. Finally, the best combination of geometrical parameters to increase the negative Poisson's ratio and extend the auxeticity region was represented.

Auxetic metamaterials, Negative Poisson’s ratio, Re-entrant hexagonal, Finite element analysis, Optimization