Analysis of deformation behavior of elliptical perforated auxetic metamaterials using a modified rotating square model

Abstract Although numerous studies have investigated the mechanical behavior of perforated auxetic metamaterials, elements, and structures, an efficient theoretical framework for quantifying the elastic properties of these extraordinary materials remains lacking. This study introduces a modified rotating square model that incorporates the deformation characteristics of auxetic materials with elliptical perforations, providing a more accurate representation of their behavior with idealized rigid square-spring–rod model. Finite element modeling of a representative unit cell of the metamaterial was employed to establish a database for parameter calibration and validation of the proposed analytical model. The results indicate that the deformation mechanism of the metamaterial is dominated by rotational deformation localized at the minimum ligaments between neighboring holes. The model predicts the elastic properties of the auxetic metamaterials with errors lower than 25%, demonstrating its effectiveness in capturing the complex deformation mechanisms of elliptical perforated auxetic structures. Additionally, the model contributes to developing design equations for lateral stiffness and shear strength in steel plate shear walls with elliptical perforated auxetic web plates. Future studies could extend the proposed model to other perforated auxetic metamaterials with various hole shapes.