[Getfem-users] Problem with Hertzian contact

[David Danan]

Dear Getfem-users,

My issue might be utterly simple, but i cannot find what i am doing wrong...

I am trying to compare the solution provided by Getfem to the analytical solution of an Hertzian contact in 2D (namely, a deformable ball against a perfectly rigid plane) but, so far, i do not get correct results.

Please, find enclosed my script. I use gmsh python api to generate the mesh but, if you do not want to use it, you can comment the line to generate the mesh in the script and juste use the mesh also enclosed.

Here are some of my concerns:

-Are the formula used in the script for the analytical contact pressure/contact surface area etc... correct in 2D?

-Is it correct to use a punctual nodal force in such a case? Does it make sense in this context?

-Is it correct to compare the analytical pressure to the lagrange multipliers?

I have also tried to use a testcase provided in Code_Aster documentation and i got much better results, although not perfect but within the tolerance given in the documentation below.
https://www.code-aster.org/doc/default/en/man_v/v1/v1.01.246.pdf

It might be because these formula are for 3D only but i am not sure yet.

Thanks in advance for your help,

kind regards,

David.

ScriptFullDisk2D.py
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Full2DDisk.msh
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