Finite Element Analysis: Captain America's Shield

Project Outline:

This project involves conducting a finite element analysis (FEA) on Captain America’s shield to simulate its behavior under applied loads. While vibranium alone is considered indestructible (and fictional), Captain America’s shield is depicted as a vibranium-steel alloy, making it extremely strong but susceptible to attainable permanent deformation under extreme conditions. Using Solidworks, this project will model, simulate, and analyze the shield’s structural performance.

  1. Create a dimensionally accurate Captain America’s Shield

  2. Research material properties and create custom material on Solidworks

  3. Determine performance and failure criteria

  4. Conduct a mesh convergence study

  5. Conduct FEA

3D CAD

Custom Material: Vibranium-Steel Alloy

Research was conducted on vibranium and steel individually to simulate the shield's behavior. Since vibranium is fictional, quantitative properties were estimated using scientific interpretations and fed into Solidworks as custom material properties. The material composition was assumed to be 60% vibranium and 40% steel. This ratio was used to calculate weighted averages for the alloy's properties:

FEA Setup

  • 3D Modeling: A dimensionally accurate model of the shield was created in Solidworks.

  • Boundary Conditions:

    • A “fixed geometry fixture” was applied to the shield’s perimeter to simulate mounting in an experimental setup.

    • A normal force was applied uniformly across the shield’s front face, varying in magnitude to observe its approach to yield point.

  • Symmetry: Symmetry was not applied in the analysis, as the simulation ran efficiently with the full model.

Mesh Convergence Study

The shield’s mesh was refined in successive steps to determine the optimal balance between accuracy and computational efficiency.

Results showed that a medium-fine mesh provided converged values with negligible differences in stress concentrations, minimizing unnecessary computational expense.

Finite Element Analysis Study

Performance Objectives

  • Withstand extreme forces without failure or loss of structural integrity; A force of 10,000,000 Newtons was applied uniformly across the front face of the shield.

  • Maintain a lightweight and thin profile for usability.

Failure Criterion

  • Maximum allowable displacement: 8 mm.

  • Factor of Safety (FOS): Greater than 1.

Simulation Results

  1. 20 mm Thickness:

    • Deformation exceeded 8 mm threshold.

    • Areas of FOS below 1 observed.

    • High likelihood of failure under extreme loads.

  2. 40 mm Thickness:

    • Maximum displacement under 8 mm.

    • FOS consistently above 1.

    • Achieved a balance between strength and usability.

  3. 50 mm Thickness:

    • Performance exceeded safety criteria.

    • Additional weight reduced usability in combat scenarios.

Limitations

The FEA was conducted for the shield design focused on static loading conditions, where forces were applied gradually and remained constant over time. While this approach provided valuable insight into the stress distribution and displacement behavior under controlled conditions, it does not fully represent the dynamic loading scenarios the shield would encounter in real-world use.

In reality, the shield would primarily face dynamic loading from high-speed impacts, such as strikes from Thor's hammer. Dynamic analysis, which accounts for factors like inertia, impact duration, and energy transfer, would better reflect the stress and displacement results under such conditions. For example:

  • Impact forces are typically applied over short durations and concentrated in specific areas, generating shock waves and vibrations. These effects were neglected in this study's simplified uniform static load assumption.

  • Without accounting for force propagation and dynamic response, the model does not capture how the shield absorbs or redistributes energy across its structure.

Project Outcomes

Results

The FEA revealed key insights into the shield’s mechanical behavior under static conditions:

  1. Stress distribution: The shield's geometry effectively redistributed stress, concentrating it in specific regions while protecting other areas from excessive strain.

  2. Displacement analysis: The shield maintained structural integrity within the defined loading parameters, with minimal deformation.

Learning

  • Limitations of static analysis: While static simulations are useful for initial designs, incorporating dynamic loading is useful for accurate prediction of real-world performance.

  • Importance of load characterization: Simulating impact forces with time-dependent parameters and localized applications would improve the model's accuracy.

  • Practical skills developed: The project honed skills in CAD modeling, meshing, and simulation setup, as well as critical thinking to identify gaps in the analysis.