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## Re: [Getfem-users] How to calculate pressure/stress tensor from displace

 From: samyak jain Subject: Re: [Getfem-users] How to calculate pressure/stress tensor from displacement in linear elasticity problems Date: Thu, 26 Jan 2017 18:47:52 +0900

Dear Kostas,

Thanks for the reply. I am using large strain law and using python language.

I have a 3D-mesh and mfu1 is the displacement fem for mesh1. CONTACT_BOUND is the region where I am trying to calculate the stress tensor.
I am trying something of this sort below. Could you please check and tell me if what I am doing is correct or not. I reshape the stress tensor into 9*(no. of dof /3) as 3-dimension tensor will have 9 components and md is model object.

`stress = np.reshape(md.interpolation("lambda*Trace(Grad_u1 + Grad_u1')*Id(3) + mu*(Grad_u1 + Grad_u1')", mfu1, CONTACT_BOUND),(9,mfu1.nbdof()/3),'F')`

Thanking You

Yours sincerely
Samyak Jain

On Thu, Jan 26, 2017 at 5:07 PM, Konstantinos Poulios wrote:
Dear Samyak

It would be helpful to know which material law you use (small or large strains?) and which programming language (python, matlab, scilab, C++?).

E.g for small strains elasticity in python, something like this should work:

mass_mat_t = gf.asm_mass_matrix(mim, mft)
for i,j in [[1,1],[2,2],[1,2]]:
sigmaij = gf.asm_generic(mim, 1, "
"u", False, mfu, md.variable("u"),
"t", True, mft, np.zeros(mft.nbdof()))
sigmaij = np.transpose(gf.linsolve_mumps(mass_mat_t, sigma))

Then sigmaij has the ij component of the stress tensor projected on the finite element space defined in mft. If mft is a Lagrangian FEM the values of sigmaij will correspond to the nodes of mft. The projection from gauss points to the finite element space is as Yves mentioned some kind of averaging.

I hope this helps.

Best regards
Kostas

On Thu, Jan 26, 2017 at 2:48 AM, samyak jain wrote:
Dear Yves,

Thanks a lot for your reply. I am not sure what you mean there. I have gone through the example and they calculate Von Mises Stress but there is already a function for that. Could you please tell me which physical quantity or _expression_ is being interpolated in that example so that I can use it as a basis for my pressure calculation. It would be really helpful if you would elaborate a bit on the usage and the example for calculating any _expression_ as I am quite new to fem and getfem. Thanks a lot.

Yours sincerely
Samyak

On Wed, Jan 25, 2017 at 6:44 PM, Yves Renard wrote:

Dear Samyak,

There is no specific function for that, but you can use the interpolation facilities of the model object. You can see an example of use for instance in the demo_thermo_elasticity_electrical_coupling example which has a  python, Matlab, Scilab and C++ version. You can interpolate any _expression_. Be aware that the stress being discontinuous across the element edges/faces, the value will be averaged.

Regards,

Yves

Le 25/01/2017 à 06:08, samyak jain a écrit :
Dear getfem-users,

I have started using getfem recently to work on few contact problems between elastic bodies.

I am able to solve few simple cases and I am able to compute displacement (u) and Von-Mises/Tresca values on my mesh nodes.

The problem I am facing is that I have to calculate pressure at the mesh points and for that I believe I need the stress tensor values at these discrete mesh points. Could someone please guide me or tell me how to get the value of these variables. I went through the documentation and checked everywhere but I couldn't find a way to calculate stress tensor/pressure.

Thanks a lot.

Samyak

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