Assigning a Local Material Axis Difference in Biphasic vs Multiphasic

[kk1101]

Hi Drs. Maas, and Ateshian,

I am genuinely sorry for being a bother. I wanted to ask a clarifying question.

When I assign an unconstrained HGO material using a biphasic material, the local coordinate axis assignment is specific to the solid material. When I assign an unconstrained HGO material using a multiphasic material, there is an option for both the overall multiphasic material and the solid material. Could you please help me understand if it is OK to just assign the local material axis to the solid component of the material? This makes sense, but I want to make sure I am understanding the software correctly.

When I "toggle the material axis", I can only see the material axis modification if I assign the local material material axis to the overall multiphasic material, not just the solid. Likewise, I cannot see the material axis in the biphasic case as the material axis is only assigned to the solid component not the overall biphasic material. I am modelling a full cylinder using a local material axis of <1,4,5>. Attached is an example of the biphasic and multiphasic cases that I am discussing. These models are not intended to run at all - I am just looking at the material axis.

I appreciate both of your time, and I am sorry if I missed something in my material axis assignment.

Thank you.

[kk1101]

Hi again,

I am sorry for the duplicate post. I wanted to update my previous post with clarification. Is there a difference if I apply the local material axis to the entire material versus just the "unconstrained HGO"? I reread Dr. Ateshian's original HGO post from 2013, and Dr. Ateshian applied spherical fiber local axis, but the overall coordinate system was applied to the overall material. I am new to the software, and I absolutely love it. But I just want to make sure I am understanding it correctly. Is there a particular reason that the biphasic and multiphasic differ? I am seeing a worrying behavior where the material axis is correct when applied to the entire multiphasic material, but not correct when just applied to the unconstrained HGO.

I am so sorry for being a bother. Thank you so much for your time and help!

[ateshian]

Hi,

For material models that provide a hierarchy of material axes, FEBio concatenates the orthogonal transformations that convert the globally-aligned-local material axes to the orientation specified in the material description. For example, if one defines an elastic mixture of fibers, one can define a local coordinate system for the mixture (so each element has orthogonal material axes that are not necessarily aligned with global axes), then the fiber-specific material axes represent fiber orientations relative to the local material axes defined in the solid mixture.

The same is true in a multiphasic material model, because sometimes the anisotropy is inherent to diffusivity (or hydraulic permeability) tensors, so it is not enough to specify material axes for the solid component of a multiphasic material.

In the example files that you shared, for the multiphasic case you speficied local material axes for the solid component (HGO unconstrained) and also for the entire multiphasic material. So, effectively, the material axes are being concatenated (in this case, the material axes of the solid component of the multiphasic material are defined relative to the material axes of the multiphasic material), so their alignment is not the same as if you had used only one set of material axes. In the multiphasic model you should remove the material axes of the "multiphasic" material, in order to reproduce the results of the biphasic material.

Having said this, I agree that the biphasic material should reproduce the same capability as the multiphasic material: It should also provide a method for specifying material axes that apply to the solid and permeability sub-materials. I'll look to fix that soon.

Best,

Gerard

[kk1101]

Thank you Dr. Ateshian! I appreciate the kind and helpful response as always.