Wave propagation in an almost incompressible material.

[Jae-Wook Jung]

Dear all,

I have some problem when I simulate wave propagation in an almost incompressible material.

As shown in below, when I loading on top of the plate in short time and using poisson's ratio as 0.3, stress wave is propagated to downward well.

https://sites.google.com/site/2013apss/home/compressible.jpg

But when I use an almost incompressible material (poisson's ratio : 0.4999996) and mixed formulation, stress wave does not propagate.

https://sites.google.com/site/2013apss/comittee/incompressible.jpg

Both cases were simulated in plane stress condition. (Only 4 corners of bottom were constrained in x,y,z direction)

Is there any reason?

And how can I make wave propagation in the almost incompressible material?

For your information, input files of two cases are attached.

Thank you for your help in advance.

[Prof. R.L. Taylor]

Two things:

First, if the material were truly incompressible the wave speed would be infinite.

You do a  nearly incompressible problem so the speed is just very high -- did you compute the MAXIMUM wave speed before you did the analysis?

Secondly, you are doing plane strain, not plane stress -- which makes a big difference in the response.  If you do plane stress you do not need the mixed element.

[Jae-Wook Jung]

Dear Prof. Taylor.

Thank you for your answer.

I already calculated wave speed in the almost incompressible material.

The wave speed is 1500m/s in that case (Calculated by Elastic modulus, mass density and poisson's ratio).

As I described before, E=5400, ν=0.4999996.

Do you think Poisson's ratio is too large to have a correct result?

Best regards,

Jae-Wook Jung

[FEAP_Admin]

There are at least two wave speeds in your problem.  Compute the P and the S wave speeds and that will give you a better idea.

[Jae-Wook Jung]

Dear FEAP_Admin and Professor Taylor,


In the almost incompressible material (E=5400, nu=0.4999996), P wave speed is 1500m/s and S wave speed is 1.34m/s.

In fact, this model is a thin box where 8 node solid elements are used (there are only two elements in the thickness direction).

The out of plane direction is without any traction, so it mimics the 2D-plane stress condition.

As shown in below, stress wave does not propagate if we increase nu to 0.4999996.



The first figure shows the time history of the stress on the top of the plate and the second one shows the stress in the middle of the plate.

On the top of the plate, stress is calculated from nodal force.

But in the middle, as shown in the figure, stress does not propagate.

Geometrical property is as follows.




Could you please let me know your opinion about whether Poisson's ratio is too large to have a correct result or not?



Best regards,

Jae-Wook Jung.