Re: [Getfem-users] Calculating Hydrostatic Pressure for Incompressible Non-Linear Hyperelastic material

[samyak jain]

Dear Kostas,

I am not sure I understood correctly what Yves and you said. I understand that material laws can give hydrostatic pressure even if there is no volume change. So does that mean the stress obtained from the model solution can contain both deviatoric and hydrostatic terms in it. 

What do you mean by adding multiplier p for incompressibility to the trace of the stress tensor. 

I am a bit confused. Could you please explain once more. Sorry for these questions but I really want to understand it correctly. 

Thanks

Yours sincerely

Samyak

On Thu, Feb 9, 2017 at 22:46 Konstantinos Poulios <address@hidden> wrote:

Dear Samyak,

As Yves has pointed out, in general one needs to add the multiplier p for incompressibility to the trace of stress tensor from the material law. This is because material laws can in general give hydrostatic pressure even if the deformation is isochoric. Hence I would suggest you to check both contributions, however I do not expect this to explain the large positive/negative values that you mentioned.

Another thing to check is a possible incompatibility between the finite element spaces for the multiplier and the displacements. A simple rule is to choose a finite element space for the multiplier of one order lower than for the displacements.

Best regards

Kostas

On Thu, Feb 9, 2017 at 1:35 PM, samyak jain <address@hidden> wrote:

Dear Kostas,

My mistake. I didn't mean to say that it is zero. I said that it is not possible to calculate that because of  incompressibility and we only get the deviatoric part and so it is zero if we try to calculate that. 

I understand that p should be the Hydrostatic pressure as I add it as incompressible brick and then use the equilibrium with boundary conditions to get the value of p but the strange part is that some of the values are positive and some negative and also they are quite high.

I have checked everything and it seems that everything else is correct.

Anyway thanks for answering. 

Yours sincerely

Samyak

On Feb 9, 2017 5:26 PM, "Konstantinos Poulios" <address@hidden> wrote:

Dear Samyak,

It is definitely not true that the hydrostatic term -1/3*Tr(sigma) should be zero in an incompressible material. If this is the case you are simply calculating the deviatoric part of sigma instead of sigma. In order to get sigma you need to add the term p*Id(3). Actually the hydrostatic term you are looking for is simply equal to p.

Best regards

Kostas

On Thu, Feb 9, 2017 at 4:20 AM, samyak jain <address@hidden> wrote:

Dear getfem-users,

I am currently trying to solve a contact problem between a hyperelastic rubber and a rigid bosy and I need to calculate the pressure values on either on the rubber.

I am using Incompressible Mooney-Rivlin Hyperelastic law and if my model I am adding also adding finite strain incompressibility brick. 

Now when I calculate Cauchy Stress from second piola kirchhoff stress, I am getting the Hydrostatic term (-1/3Tr(sigma)) of the cauchy stress tensor as zero which is what it should be as the material is incompressible.

So, is there a way is getfem to calculate the hydrostatic pressure term for such incompressible materials.I believe treating the material as nearly incompressible (Poisson's ratio 0.499) is one way to solve it but I don't know how it works or if it is implemented in the model.

Could you guys please provide any help or suggestion to calculate the hydrostatic pressure for such a case.

Thanks a lot.

Yours sincerely

Samyak

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