Free Swelling Effect

[Shamimur Akanda]

Hello,

I want to add a free swelling effect (unloaded) on cartilage followed by a creep test. What approach do you suggest for modeling it? I am more eager to use Donnan equilibrium swelling material in solid mixture. An elaboration of this approach would be highly appreciated Thank you in advance.

Regards,

Shamimur

[ateshian]

Hi Shamimur,

You can use a biphasic analysis where the solid material is a solid mixture consisting of a ground matrix (e.g., neo-Hookean) and a Donnan equilibrium material.

You can set up your analysis to have two steps: (1) A steady-state analysis to allow swelling, followed by (2) a transient analysis for loading.

Depending on the type of geometry you are examining, the swelling step may deform the biphasic material in a way that might affect how you apply the creep load in the transient step. So I suggest you examine the results of the first step before deciding how to apply the creep load in the second step.

Best,

Gerard

[Shamimur Akanda]

Hello Dr. Ateshian,

Thank you very much for your input. My solid mixture will also consist of fibers, Neo-Hookean matrix and Donnan equilibrium materials. Is there any specific boundary condition that I need to implement for the swelling condition?

Regards,
Shamimur

[ateshian]

Hi Shamimur,

There are no specific boundary conditions needed to implement the swelling condition when using the "Donnan equilibrium" material. Instead, to cause the swelling, you need to attach a load curve to the relevant properties of that material (either cF0 or bosm) to cause swelling by altering the Donnan osmotic pressure, as explained in the User's Manual.

Best,

Gerard

[Shamimur Akanda]

Hello Dr. Ateshian,

Thank you very much for you reply. I have been trying to conduct swelling on my model. But the model is diverging everytime. If possible, can I send you the model via email?

Regards,
Shamimur

[ateshian]

Hi Shamimur,

Yes, you can email me the model if you are unable to post it on the forum. Please keep in mind that it is harder and more time-consuming for me to examine very large models, so please try to limit the size of the model you send me.

Best,

Gerard

[ateshian]

Hi Shamimur,

I looked at the file you sent me and here are a few things I needed to do to make it run to completion:

1) You have two steps, the first is steady-state swelling and the second is transient loading. For the first step you want your platen (Material2) to remain stationary, but your model actually restricted only five degrees of freedom, leaving the loading direction free. You should create a fully-fixed rigid constraint and place it in the first step, and copy your existing constraint for that platen to the second step. This will allow the model to converge properly in the first step (swelling cartilage against a stationary platen) and in the second step (loading applied to the platen).

2) For the Donnan equilibrium material, you set cF=150 but you also attached a load curve to cF which varies from 0 to 300. This means that you are raising cF to 150 x 300 = 45000. You should let your load curve vary from 0 to 1.

Other minor changes:
(a) There is no need to use a tied-biphasic interface between the biphasic layer and the rigid substrate (Material1). You can use a rigid contact to achieve the same result (and select the back of the biphasic layer).
(b) There is no need to a use multiphase analysis for this problem, a biphasic analysis should suffice.
(c) During the steady-state swelling response, you should set ptol=0 and ctol=0 (if you use a multiphasic analysis) and rely only on a non-zero dtol convergence parameter.
(d) You can run the steady-state response in 10 steps instead of 100 (once you fix the issue with the cF load curve).

Best,

Gerard

[Shamimur Akanda]

Hello Dr. Ateshian,

Thank you very much for your detailed reply and your time. I will implement your suggestions in my model

Shamimur