Investigating mechanical properties and bending behavior of an auxetic plate with 4-star unit cell

Abstract

This study derives the constitutive relationships between stress resultants and strain measures for 4-star auxetic structures using force-moment analysis of a representative unit cell and the Castigliano strain energy method. To validate the accuracy of the constitutive model, bending analysis is performed for a 4-star auxetic rectangular plate under Levy boundary conditions. The analytical and numerical results show excellent agreement, confirming the validity of the constitutive relations extracted from the generic 4-star unit cell. This work establishes a theoretical framework for designing 4-star auxetic metamaterials and demonstrates their potential for diverse engineering applications.