I came across this form of damping implemented in an elastodynamics problem.
The stress tensor without the damping would look like:
$ \sigma = 2 \mu \epsilon + (\lambda \, \text{tr} (\epsilon)) I $
where, $\mu$ and $\lambda$ are Lame' parameters dependent on the Young's Modulus and the Poisson's ratio. Trace is represented by '$\text{tr}$', and $\epsilon = (\nabla u + {(\nabla u)}^T)$ is the strain tensor. Here, $I$ is the second order identity tensor.
I have the following questions:
- What is this type of damping called?
- Does $\eta$ control the damping %? For eg. should $\eta = 0.1$ mean 10% damping? I don't think it works like that though.
- Any other comments on this type of damping?
I ran some wave propagation simulations based on this type of damping and observed the following in Paraview for $\eta=0$ and $\eta=1$. I don't see substantial difference in the displacement values. It is 17% for the highlighted point. Any observations/comments from experts will be useful. Please click on the picture to enlarge it.
Thank you!