Mechanical analysis of Captain America's shield using composite materials modeling and plate theory

Abstract

In the field of composite materials theory and solid mechanics, a fictitious steel-vibranium alloy was considered, its effective elastic modulus obtained using the Voigt-Reuss-Hill (VRH) method. From the macroscopic data of the shield (mass 5.44 kg, diameter 76 cm), the effective density, a thickness of 1.64 mm, and an elastic stiffness of approximately 191.7 GPa were determined, allowing the calculation of flexural stiffness and deflections under load using classical thin-plate theory. Sensitivity analysis showed that the volume fraction, modulus, and density of the vibranium directly influenced the overall stiffness, thickness, and impact absorption capacity. Three-dimensional simulation in Fusion 360, with loads up to 45.5 kN, demonstrated that the shield operated entirely within the elastic range, with maximum Von Mises stresses below 96 MPa and displacements less than 0.2 mm, confirming efficient stress distribution and high structural strength. Overall, the model suggests that the steel-vibranium shield exhibits performance comparable to advanced aerospace materials, validating the physical feasibility of the behavior attributed to the shield in fiction.