Methods for Damping High Frequencies in FEM Thin Film Model?

• Leyic
In summary, the high frequency oscillations in the simulation appear to be due to the use of a simplified model for polymers.
Leyic
I would like to simulate the vibrations of a thin film polymer in vacuum using nonlinear analysis. For this purpose I am using an FEM program I have written in MATLAB. I do not have any data regarding damping in the structure, so I am estimating the damping using stiffness-proportional-only Caughey damping and adjusting the damping ratio until results appear reasonable. This strategy seems to be working for finding the steady-state result, but does nothing for the high frequency oscillations induced by the discretization. This is revealed in the series of figures below:

The above plots appears reasonable, but upon zooming in on the lower plot:

a high frequency, low amplitude oscillation is revealed. Zooming in further:

shows that this oscillation is not damped out, but persists at a non-relevant scale. This causes the simulation to run slow even after steady-state should have been achieved.

I have made one attempt to work around the issue by introducing artificial static friction to cause nodes to stick when near steady-state, but this only induces the oscillations to grow (thought to be due to compounding forces from neighboring non-stuck nodes).

Is there some other approach I could take to damp the high frequency oscillations? A non-exhaustive search of academic literature via Google only turned up results on Rayleigh damping and elementary viscoelastic models. If there is some terminology specific to this particular problem, I am not aware of it.

What physical model of the film have you used ?

I am currently using a hyperelastic linear stress-strain relationship with full nonlinear Eulerian strain and a modification that compressive stresses are forcibly set to zero. The FEM model regards each element as a 2D membrane.

I realize this is not a particularly accurate model for polymers, but as I am writing my own program, I only want to increase the complexity as I can manage to have simpler models work appropriately.

1. What is the purpose of damping high frequencies in a FEM thin film model?

Damping high frequencies in a FEM thin film model is important because it helps to reduce the oscillations and instability in the model, resulting in more accurate and stable results. It also helps to prevent the model from diverging or becoming numerically unstable.

2. What are some common methods for damping high frequencies in a FEM thin film model?

Some common methods for damping high frequencies in a FEM thin film model include using higher-order elements, adding viscous damping, using modal damping, or implementing a time integration scheme with damping.

3. How does higher-order elements help with damping high frequencies?

Higher-order elements have more nodes and thus allow for more accurate representation of the shape and behavior of the model. This can help to reduce the high frequency oscillations and provide more stable results.

4. What is viscous damping and how does it work?

Viscous damping is a method where a damping term is added to the equations of motion in the FEM thin film model. This damping term is proportional to the velocity of the element and helps to dissipate energy and reduce the high frequency oscillations.

5. Can time integration schemes with damping be used for all FEM thin film models?

Yes, time integration schemes with damping can be used for all FEM thin film models. However, the appropriate damping coefficient and integration method may vary depending on the specific model and its characteristics.

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