Analytical and Numerical Approach for Determining the Mechanical Properties of a Novel 3D Double Arc Star-Shaped Structure with Two Different Cross-Sections

Auxetic materials, characterized by their negative Poisson's ratio (NPR), exhibit unique mechanical properties that make them highly desirable for lightweight structural applications. This study introduces a novel 3D double arc star-shaped (3D DASS) auxetic structure and systematically investigates the influence of cross-sectional shape (square vs. circular) and thickness variation on its mechanical behavior. We derive expressions for Poisson's ratio and Young's modulus using analytical modeling and numerical simulations and validate them across different geometric configurations. The results reveal that while Poisson's ratio remains nearly constant for both cross-sections, Young's modulus is significantly influenced by cross-sectional thickness, particularly in circular configurations. These findings provide valuable insights into the design optimization of lightweight auxetic structures and their potential applications in engineering.