Post-processing contact pressure and force using augmented Lagrangian method in GetFEM

General
1

Hello everyone,

I am currently working on a 3D contact mechanics problem using the augmented Lagrangian method.
For post-processing purposes, I would like to compute the contact force and the contact pressure. The multiplier is introduced in the model using:

md.add_filtered_fem_variable("lam2", mfl2, region);

However, I’m having trouble evaluating the contact pressure only on the contact surface.
I tried using interpolation, but my output gf.MeshFem is defined over the entire mesh, whereas I need it only on the contact surface.

  1. What is the proper way to project or interpolate the contact pressure over the contact surface (i.e., the region used with add_filtered_fem_variable)?
  2. What is the recommended way in GetFEM to evaluate and export the total contact force based on the Lagrange multiplier?

Thank you very much for your help!

Best regards,
Rene

1 Like
2

You can have results on any mesh and export them on any other mesh. Here some examples for inspiration.

mfx_ = gf.MeshFem(m, 1)
mfx_.set_classical_fem(1)
kept_dofs = mfx_.basic_dof_on_region(RG1)
mfx = gf.MeshFem("partial", mf_, kept_dofs)

md.add_fem_variable(mfx)

mfout.export_to_vtu("results.vtu",
                    mfout, md.interpolation("H", mfout), "H",
                    mfout, md.interpolation("sqr(H)", mfout), "H_squared",
                    mfp, md.variable("P"), "P",
                    md.mesh_fem_of_variable("u"), md.variable("u"), "displacements",
                    mfx_, mfx.extend_vector(md.variable("x")), "x",
                    mfout, md.interpolation("x", mfout, RG1), "x in region 1",)

When you express surface results on a volume mesh, the result decays in the first element below the surface towards 0. This is normal and it is just a visualization convention.

Results can also be exported on so called “Slices”, which offer quite some post-processing capabilities within GetFEM:

Nowadays I prefer to do this kind of post-processing in ParaView, and I rarely use slices.

3

Thank you very much for your valuable response it was truly helpful.
Just two quick side questions, not directly related to this topic:
Is there a way in GetFEM to compute the volume of an arbitrary shape?

I’ll get back to you if I have any further questions.
Thanks again!

Best regards,
Rene

4

If mim is an integration method on some mesh m, then the total volume of the mesh can be computed with

VOL = gf.asm_generic(mim, 0, "1", -1)

The x-coordinate of the center of mass of the mesh can be computed with

x_pos = gf.asm_generic(mim, 0, "X(1)", -1) /  VOL

The area of some surface region RG_SURF of the mesh, can be computed with

A = gf.asm_generic(mim, 0, "1", RG_SURF)
1 Like
5

Thanks it works perfectly