Cauchy ou Piola-Kirchoff stress?

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Groguigui
Posts: 25
Joined: Thu Mar 09, 2017 2:13 pm
Location: Lille

Cauchy ou Piola-Kirchoff stress?

Post by Groguigui »

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Hi everybody,

I would like to develop some hyperelastic incompressible models with calculix in my laboratory, but before this, it is necessary to test calculix.

For this, I do some simple cases like tensile test (simple and bi-axial) and calculix result are always differents of analytic result (and COMSOL Multiphysics results) for Neo Hookean or Yeoh model and 3D problem.
So, I ask some questions at Guido Dhondt :
1) Do you know why?
2) What's happening exactly? Can you tell me how Calculix solve hyperelastic problem?
I know that Neo Hookean is not good to solve a bi-axial hyperelastic problem, but I do that to understand how calculix solve this problem and why even with Yeoh model our results are differents.
3) Is it a problem with a Cauchy tensor?
4) With hyperelasticity, is it better to use *DLOAD or *CLOAD?
and he has replied me this following message :
the background of the hyperelastic implementation is described in detail in my
book (Wiley 2004, cf. website http://www.dhondt.de). It involves a straight
differentiation of the 2nd Piola-Kirchoff stress w.r.t. the Lagrange strain
tensor (CalculiX uses a total Lagrangian approach).

The stresses which are reported in the .frd-file are Cauchy stresses.
I am moderately satisfied with this answer because even if Calculix calculates differently from the analytic, strain results must be the same (I have a noticeable difference of 20% !!!).
So I come to ask you:
1) In FreeCAD, are the true constraints displayed (in the sense of Cauchy in Eulerian) or those of Piola-Kirchoff (in Lagrangian)?
2) What is his Von Mises based on?
3) Do you have any idea of where such discrepancies could arise?
4) The difference may also be the interpretation of the force applied between CLoad and DLoad, which then seems the most correct?

I suppose DLOAD is better with large deformation, but it is more difficulte to converge.

Thanks
sodelo
Posts: 73
Joined: Tue Jan 24, 2017 9:20 am

Re: Cauchy ou Piola-Kirchoff stress?

Post by sodelo »

Hi Groguigui,

Guido is really the best guy to answer your questions. He is obviously very good in his field.

Could you please describe your reference solution and how you want to simulate it with Calculix? There are many opportunities to make mistakes.

Freecad just displays Calculix results. So Cauchy stresses are used. If you want to introduce a homogeneous stress within a specimen, I would advise:
- either to impose a displacement on all the nodes at one extremity,
- or impose a negative pressure (same than to introduce a stress).

To implement a constitutive law, your best call is to use MFRONT (tfel.sourceforge.net), which is a dedicated language and tool for this kind of implementation. It is interfaced with several FE codes including ABAQUS and Calculix.

Good luck!
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Groguigui
Posts: 25
Joined: Thu Mar 09, 2017 2:13 pm
Location: Lille

Re: Cauchy ou Piola-Kirchoff stress?

Post by Groguigui »

Thanks Sodelo,
Guido is really the best guy to answer your questions. He is obviously very good in his field.
I have already ordered his book. ;)
Could you please describe your reference solution and how you want to simulate it with Calculix?
What do you mean by "reference solution"?
To simulate a testile test, I apply 3 symmetries on the cube, and CLoad on other face (because DLoad didn't converge). Material is totally hyperelastic, with Neo Hookean model or Yeoh model.
Freecad just displays Calculix results. So Cauchy stresses are used. If you want to introduce a homogeneous stress within a specimen, I would advise:
- either to impose a displacement on all the nodes at one extremity,
- or impose a negative pressure (same than to introduce a stress).
Thanks for your advise, it is not applicable for my cases but that is interessing. I will test that.

I would like to simulate a round shell, and apply pressure orthogonally to test bi-axial traction with hyperelastic incompressible material. Abaqus is not good with this problem (strain 20% max before to diverge), but calculix can solve a big strain (over 200% of strain). That is very weird, because with incompressible shell how volume is conserve?
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