Hertz contact with force control


I am trying to analyze a simple Hertz contact problem in 3D - sphere (or actually half of a sphere because the top part is not needed) on a flat plate. I use symmetry in two planes and the plate is fixed on the bottom face. However, because of the fact that I want to apply force to the sphere instead of using prescribed displacement, there’s one rigid body motion left that prevents the analysis from converging. Contact should eliminate it but apparently, it’s not properly established at the beginning of the analysis. Both parts are touching initially but just at one point (as always with such geometry). In Abaqus I would use stabilization functionality that applies some damping to support the model until the contact is fully established. But it seems that there’s no option like that in CalculiX. Are there any workarounds ? How would you handle such a problem ?

Could you attach a spring to eliminate this rigid body motion?

Thanks for the reply. The preprocessor that I use doesn’t support discrete springs and dampers and I’d rather avoid them for now because this simulation should be as simple as possible - it will serve as a tutorial.

I was thinking about other two tricks that I use in Abaqus:

  • move the parts a bit towards each other so they are in small initial interference that can be resolved by ADJUST
  • define additional step (prior to the one with force) and use small prescribed displacement in this step to establish contact (the problem is that it could change the results and the whole point is that I want to verify them with analytical solution)

Would this work in CalculiX ? Are there any other potential workarounds here ?

i have used a spring, and i have forced the system by having one common nodes for master and slave part with a 2-D modeling

Maybe old:






If you start with displacement control and then switch to force control, the final result should not depend on the prescribed displacement, at least if the model is elastic and frictionless.

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Thank you. I thought that stresses will accumulate over both steps and the second step will start from already deformed and stressed configuration from the end of the first step.

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If your model is elastic, the stresses won’t depend on load history. The contact status, however, can be history dependent.

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