Incompressibility in Hyperelastic Material Model


#1

Hi,

I was trying to run some simulations using the Hyperelastic material model that have been introduced in SimScale recently. I am trying to run these for the SimScale blog article.

The interface allows for input of D1 parameter and allows this for any poisson ratio. However, if the poisson ratio is >0.4, the normal elements should demonstrate locking effects. This should be especially pronounced as it reaches 0.49 or 0.49999 etc. This would require mixed or enhanced formulation or reduced-integration elements to prevent locking.

Does SimScale automatically detect such a high poisson ratio & use a mixed or enhanced formulations? Because it did not show any such options for selection. In Abaqus, it allows one to choose these elements. So I was wondering, if SimScale is doing this automatically?

Thanks
Ajay


#2

Hi Ajay (@aharish)!

The D1 refers to the incompressibility factor. The lowest the value, the more incompressible material will be. But making it low enough normally leads to divergence.

You are right about the locking effect. Unfortunately, SimScale don’t detect this effect automatically. Whereas, you can avoid this by using reduced integration scheme under tree item Mesh.

But as I already mentioned, make sure the value of your D1 is not low enough otherwise you may run in to convergence problem.

I hope this help. If you have any question/s, feel free to ask.

Best,
Ahmed


#3

Dear Ahmed,

Thank you very much for the informative reply. Thank you for pointing out about reduced integration. I am sure incompressibility constraint is not simple to solve & SimScale is working on this.

I agree that D1 = 2/K and as K increases (or otherwise poisson ratio approaches 0.5), there will be volumetric locking and this could lead to lack of convergence. Higher-order elements could be a solution. Reduced integration could also be one solution but in some cases this can also lead to hour-glassing?

Do you think a Q1P0 formulation would be something coming in the near-future? That is a quite stable element especially concerning incompressible problem. It does have problems in bending dominated problems but sufficient refinement can solve the shear locking issues.

Thanks
Ajay


#5

Dear Ahmed

Here is a link to a pdf presentation on Q1P0 and its implementation. Its a mixed element. It does not satisfy the BB-condition but is extremely stable for most problems.

Link: http://cedricthieulot.net/notes.pdf

Cheers
Ajay


#6

Hello @aharish,

as @ahmedhussain18 pointed out, currently we are limited to reduced integration elements for nearly incompressible materials (be sure you are using a second order mesh in case you are using reduced integration elements).

For the future we will also introduce mixed elements with two (P2P1 or P1P1) and three (P2P1P1) field formulations (displacement, pressure, swelling).
I’ll keep you updated once those have been released.

Best,
Richard