Novel reentrant auxetic meta-structure inspired by spider silk microstructure: analytical investigation on mechanical properties

This study introduces a novel bio-inspired microstructure, the Reentrant Spidroin Element (RSE), inspired by the remarkable mechanical properties of spider silk. This work proposes a reentrant auxetic structure incorporating the RSE to investigate its mechanical behavior, specifically focusing on its Poisson’s ratio and Young’s modulus. The design leverages the unique auxetic property of a negative Poisson’s ratio, which enables the material to contract perpendicularly to the direction of compression and expand perpendicularly to the direction of tension. This characteristic offers significant potential for applications in fields such as biomedical engineering, aerospace, and flexible electronics. The mechanical properties of the RSE are derived analytically using curved beam theory and Castigliano’s theorem, providing a robust framework for modeling the unit-cell’s deformation behavior based on its geometrical and material parameters. Key geometrical parameters—including the initial length and radius of the spidroin element, and a secondary length parameter—are systematically analyzed to understand their influence on the auxetic behavior and stiffness of the structure. The analytical model is validated through finite element analysis (FEA), which demonstrates excellent agreement between theoretical predictions and numerical simulations (with a maximum relative deviation below 0.5%), thereby confirming the reliability and accuracy of the proposed mathematical framework.