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

[Yves Renard]

Dear Samyak,

May be to be more precise, I would add that if you use the finite strain incompressible law, then the multiplier (call it lambda)  used to prescribe the incompressiblity constraint is to be added to the spheric part of the Hyperelastic Law used

sigma = Hyperelastic_law_used - lambda Id(3)

So that the hydrostatic pressure is -1/3*Tr(sigma) contains two terms.

Yves.

Le 09/02/2017 à 09:26, Konstantinos Poulios a écrit :

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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  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
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