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## Eigenfrequency issue of soft elastomer (PDMS)

Posted Apr 9, 2012, 9:30 PM EDT Structural Mechanics & Thermal Stresses 5 Replies

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

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 AM EST