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Eigenfrequency issue of soft elastomer (PDMS)

Posted Apr 9, 2012, 9:30 p.m. EDT Structural Mechanics 5 Replies

Chris Layman
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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
5 Replies Last Post Mar 7, 2013, 11:16 a.m. EST
Chris Layman
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Posted: 1 decade ago Apr 16, 2012, 2:50 p.m. EDT
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
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
Yuhao Liu
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Posted: 1 decade ago Mar 6, 2013, 7:52 p.m. EST
did you work out the problem to eliminate other modes?
did you work out the problem to eliminate other modes?
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Mar 7, 2013, 11:10 a.m. EST
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
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
Chris Layman
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Posted: 1 decade ago Mar 7, 2013, 11:12 a.m. EST

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

[QUOTE] 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 [/QUOTE] Sorry for the confusion, 1042 is the material density of PDMS
Chris Layman
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Posted: 1 decade ago Mar 7, 2013, 11:16 a.m. EST

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
[QUOTE] did you work out the problem to eliminate other modes? [/QUOTE] 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

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