A problem of the solid volume fraction in biphasic material

[albert22]

Hello,

I used biphasic material with perm-Holmes-Mow permeability to study the influence of the sold volume fraction. In ‘test 1’, the solid volume fraction is 0.1923. In ‘test 2 fraction0.01’ and ‘test 3 fraction0.9’, I changed the solid volume fraction from 0.1923 to 0.01 and 0.9 respectively.

However, the results did not show clear differences among these tests. Does it correct? I suggest that it should exists some differences (such as fluid pressure) between test 2 and test 3 because the solid volume fractions are so different.

I also used the same method to test biphasic material with perm-ref-iso too. And this time the results show different trend.

So I don't know why it didn't work in the first materail setting (biphasic material with perm-Holmes-Mow permeability). I had read the FEBio-user’s manual but I still could not figure it out. I attached my models in the attachment. I would really appreciate it if anyone could help me. Thank you in advance.

Albert


test solid fration(perm-Holmes-mow).zip

[ateshian]

Hi Albert,

The permeability in the Holmes-Mow model varies as a function of the relative volume J. If you save this plot variable and display it, you will find that J is initially nearly equal to 1 upon loading (because the pore volume cannot decrease instantaneously), and by time t=300 (the final time step in your analysis) it ranges from 0.93 to 1.04. Over that range, the various values of phi0 that you have tried do not produce significant differences in the permeability k, see perm_albert22.png.

If you allow the analysis to run longer, J will change by a larger amount as the fluid leaves the pores of the biphasic material, thereby reducing their volume. So there may be a small variation in the temporal response between your models as the analysis reaches equilibrium (zero fluid pressure and zero solid velocity).

Keep in mind that the perm-Holmes-Mow material does not allow J to drop below phi0 (which is the limiting case when the pore volume reduces to zero). So, for your model that uses phi0=0.9 you will encounter numerical problems as J decreases toward 0.9.

I also used the same method to test biphasic material with perm-ref-iso too. And this time the results show different trend.

This material model allows the permeability tensor to become anisotropic as the deformation progresses, as long as k1r and k2r are not equal to 0. Without further information on the exact properties you used for this model, and the different trends you observed, I am unable to provide more feedback.

Best,

Gerard

[albert22]

Hi Gerard，

Your explanation helps a lot. Now I know the reason. Thank you so much.


Best,

Albert