Eigenfrequency issue of soft elastomer (PDMS)

Thread index  |  Previous thread  |  Next thread  |  Start a new discussion

RSS FeedRSS feed   |   Email notificationsTurn on email notifications   |   5 Replies   Last post: March 7, 2013 4:16pm UTC
Chris Layman

Chris Layman

April 10, 2012 1:30am UTC

Eigenfrequency issue of soft elastomer (PDMS)

Hi,

Coming across this issue doing elastic wave band structure calculations. Starting with a simple square unit cell of a single isotropic material (no scatterers), with periodic boundary conditions. Perform an eigenfrequency for a fixed wave vector, say for aluminum as the material. The first two eigenfrequencies (for a non zero wave vector) should correspond to the shear wave and longitudinal wave speeds in the bulk material. This works fine and I get the right numbers for aluminum or another other standard material (steel, pmma etc)

Now when I use values for a soft elastomer like PDMS, such as E = 1.95e6, vu = 0.4997 and 1042. The first eigenfrequency does match the shear speed (and 25 m/s) but then there are countless other modes which don't seem to have any physical meaning. If I solve for say 500 eigenfrequencies, I just get almost a continuum of states and the band profile is useless. I need to include the small, but important shear modulus, so I can't model this as a fluid.

It seems it must be an issue with the Poisson ratio so close to 0.5, because if I start lowering vu, the band profile becomes more and more accurate.

I have tried using a Neo-Hookean model and also using the U-P formulation for nearly incompressible materials, it doesn't help.

Has anyone run into this ?

Thanks
Chris

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

Chris Layman

Chris Layman

April 16, 2012 6:50pm UTC in response to Chris Layman

Re: Eigenfrequency issue of soft elastomer (PDMS)

Just to possibly answer my own question. I think the issue is that in this case, when the shear wave speed is so low, it creates multiple band folding back into the first BZ. It's not an issue with the elasticity matrix as I initially thought. Still though, this makes the analysis of the band diagram problematic.

If anyone is doing problems like this, let me know.

~Chris

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

Yuhao Liu

Yuhao Liu

March 7, 2013 12:52am UTC in response to Chris Layman

Re: Eigenfrequency issue of soft elastomer (PDMS)

did you work out the problem to eliminate other modes?

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

Nagi Elabbasi

Nagi Elabbasi
Certified Consultant
Veryst Engineering

March 7, 2013 4:10pm UTC in response to Yuhao Liu

Re: Eigenfrequency issue of soft elastomer (PDMS)

If I understand you correctly the 1042 number you provided is a (very low) shear modulus, G. That is the cause of the “folding” not the fact that the material is nearly incompressible. If you use the G of an isotropic material = E/2/(1+nu) the longitudinal natural frequency should be of the same order of magnitude as the shear frequency.

Nagi Elabbasi
Veryst Engineering

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

Chris Layman

Chris Layman

March 7, 2013 4:12pm UTC in response to Nagi Elabbasi

Re: Eigenfrequency issue of soft elastomer (PDMS)


If I understand you correctly the 1042 number you provided is a (very low) shear modulus, G. That is the cause of the “folding” not the fact that the material is nearly incompressible. If you use the G of an isotropic material = E/2/(1+nu) the longitudinal natural frequency should be of the same order of magnitude as the shear frequency.

Nagi Elabbasi
Veryst Engineering


Sorry for the confusion, 1042 is the material density of PDMS

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

Chris Layman

Chris Layman

March 7, 2013 4:16pm UTC in response to Yuhao Liu

Re: Eigenfrequency issue of soft elastomer (PDMS)


did you work out the problem to eliminate other modes?


One way around this is to model PDMS as a fluid, but if shear effects are needed than you're stuck with all those modes.

~Chris

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse


Rules and guidelines