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Re: [Getfem-users] Problem with Hertzian contact

From: Konstantinos Poulios
Subject: Re: [Getfem-users] Problem with Hertzian contact
Date: Fri, 6 May 2022 09:23:34 +0200

Dear David,

With the attached script you should also be able to reproduce the results for the first example of our paper
(the script is only slightly modified compared to the original one, so that it can run on python3 and the current version of GetFEM).

Best regards

On Fri, May 6, 2022 at 8:45 AM Konstantinos Poulios <> wrote:

Your script looks very nice and clean. It just needs a bit of fiddling with the augmentation parameter and the solver. The attached version produces this result

Just some general comments:
- Point constraints/loads make almost never sense (unless you know beforehand the reaction force at a constrained point will be zero)
- Maybe there is some issue with your units, I needed to increase the load to a very large value to get some visible deformations
- The Saint-Venant Kirchhoff material law, that we often use for demonstrations, is a "toy" material law. If you do anything with moderate/large strains, use some proper hyperelastic law
- The augmentation parameter should be in the same order of magnitude like the modulus of elasticity, from 1-2 orders of magnitude below to 1-2 orders of magnitude above.

Best regards

On Thu, May 5, 2022 at 8:04 PM David Danan <> wrote:
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.
It might be because these formula are for 3D only but i am not sure yet.

Thanks in advance for your help,
kind regards,

Description: Text Data

Attachment: half_disc_Q1.msh
Description: Mesh model

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