Zero-energy modes – also referred to as zero eigenvalue modes – occur when the discretized system is underdetermined or cannot be solved uniquely. This means that there are more degrees of freedom (unknowns) than equations available. Mathematically, zero-energy modes are special solutions of the system of equations associated with an eigenvalue of zero. Thus, this mode can be activated without energy supply and, potentially, a deformation without strain occurs.
As zero-energy modes can lead to model instability and unphysical solutions, several methods are advisable in RFEM to prevent this problem.
- Higher-Order Elements: Zero-energy modes are more likely to occur in lower-order finite elements (e.g. linear elements). Consider using higher-order elements (e.g. quadratic or cubic elements) for your analysis. Higher-order elements provide better accuracy and are less prone to zero-energy modes.
- Mesh Refinement: Ensure that your mesh is sufficiently refined, especially in areas with high stress gradients or complex geometry. A fine mesh can help capture the deformation more accurately and reduce the likelihood of zero-energy modes.
- Material Properties: Ensure that you have assigned suitable material properties to your model. Incorrect material properties can lead to unrealistic behavior and potentially cause zero-energy modes. Double-check the material parameters and properties.
- Boundary Conditions: Verify that your boundary conditions are correctly applied. Improper boundary conditions can cause zero-energy modes. Ensure that all degrees of freedom are correctly constrained or loaded.
- Solver Settings: Review the solver settings in RFEM. Some solvers have options to stabilize the analysis and prevent zero-energy modes. Adjust the solver settings to use stabilization techniques if available.
- Damping: Introduce damping into your analysis if necessary. Damping can help stabilize the analysis and prevent zero-energy modes. However, use damping judiciously to avoid introducing artificial damping that affects the accuracy of results.
- Check Geometry: Ensure that your model geometry is correct and free of errors. Small gaps or overlaps in the geometry can lead to numerical issues, including zero-energy modes.
- Sensitivity Analysis: Perform sensitivity analyses to identify critical parameters or areas that might be more susceptible to zero-energy modes. You can then take specific actions to address these areas.