Re: [Getfem-users] How to calculate pressure/stress tensor from displacement in linear elasticity problems

[Konstantinos Poulios]

Dear Samyak,

That "sigma" was a typo of mine, it should simply be "sigmaij", i.e. the outcome of the previous command.

"mft" is the mesh_fem object that you would like to get the result on. It could be the same as mfu but with qdim=1 (scalar) or it could be a different finite element space. E.g. you could have a quadratic mfu and a linear mft, or mft could even be discontinuous.

"t" is a temporary variable used for the assembly. Its value doesn't matter because it appears only as a test function "Test_t". In the provided code snippet it is set to np.zeros(mft.nbdof()) because GetFEM++ requires some value.

Best regards

Kostas

On Fri, Jan 27, 2017 at 3:42 AM, samyak jain <address@hidden> wrote:

Dear Kosta,

In your equation below, could you explain me few things.

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, "({Lambda}*Div_u*Id(qdim(u)) + {Mu}*(Grad_u+Grad_u'))({i},{j})*Test_t".format(Lambda=Lambda, Mu=Mu, i=i, j=j), -1,
                           "u", False, mfu, md.variable("u"),
                           "t", True, mft, np.zeros(mft.nbdof()))
  sigmaij = np.transpose(gf.linsolve_mumps(mass_mat_t, sigma))

1) Could you please explain the terms/variables mft, "t", "sigma".

Also,  I believe your _expression_ above is for a 2D case.

Thanks

Yours sincerely
Samyak Jain 

On Thu, Jan 26, 2017 at 7:27 PM, samyak jain <address@hidden> wrote:

Dear Kosta,

I will try the projection method you mentioned in your previous mail. I am using 'add_integral_large_sliding_contact_brick_raytracing' and then I am adding slave and master brick with boundary conditions for my contact problem. Actually I need to calculate pressure everywhere and not just the contact region. I just tried to calculate in on the contact surface. I will try the projection method you mentioned and will let you know how it goes.

Thanks for your help.

Yours sincerely
Samyak

 

On Thu, Jan 26, 2017 at 7:21 PM, Konstantinos Poulios <address@hiddenom> wrote:

Dear Samyak

The projection method of my previous mail works also for large strains if you simply replace the _expression_ for the stress tensor with the corresponding one. Of course, as you suggested you can also do an interpolation instead of projection, but then you depend on the averaging that the interpolation function of GetFEM++ will do behind the scene for the discontinuous field that you are working with. I have never tried it on a surface, so I cannot say how it works.

But if you care only about the contact interface, why don't you simply use the Lagrange multiplier which already describes the traction on this surface? Which contact algorithm do you use?

Best regards

Kosta

On Thu, Jan 26, 2017 at 10:47 AM, samyak jain <address@hiddenom> wrote:

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 <address@hiddenom> 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, "({Lambda}*Div_u*Id(qdim(u)) + {Mu}*(Grad_u+Grad_u'))({i},{j})*Test_t".format(Lambda=Lambda, Mu=Mu, i=i, j=j), -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 <address@hiddenom> 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 <address@hiddenfr> 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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  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
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