Hello,
It looks similar to a 3 point bend test which I did a while back.
I have a few observations regarding your meshes.
Mesh.med is bad for analysis. I believer you used "allow quads" in NetGen Parameters which makes it generate a mix of quad and tri elements on punch half cylinder. Also It creates Pyramid elements in punch which are bad for convergence.
The half cylinder(punch ) is a sweepable body and any other software will recommend swept mesh with base face as a quad dominated mesh. Or choose an all tetra mesh like in ML_2.med or ML_3.med
I don't have access to old version of CA(like 16.2) I ran it with simvia-17.4.0
Regarding comm file:
YOu used FORCE_NODALE on F_1. In my view, FORCE_NODALE is very unstable way to push the cylinder down on rectangular beam. I believe If the mesh density is not uniform like a perfect grid (as is case here on F_1which has tri3 element), we might get inplane moments with FORCE_NODALE which can cause convergence issues.
If your ultimate aim is to push down cylinder vertically while making contact with long beam, I prefer use imposed displacements with AFFE_CHAR_MECA(or better yet AFFE_CHAR_CINE). So changing to
load = AFFE_CHAR_MECA(DDL_IMPO=_F(DX=0.0,
DZ=0.0,
DY =-10,
GROUP_MA='F_1'),
MODELE=MODEL)
The simulation converges for any value of DY (10 , 20 ,30 etc) imposed on F_1.
Next I changed timestepping to be 10 increments until 1 sec.
I changed ALGO_CONT and ALGO_FROT from PENALISATION to STANDARD and it converged fine. STANDARD is better than PENALISATION in terms of accuracy.
I swapped Master and Slave surfaces. Simulation works well for both ML_2 and ML_3 meshes.

ave faces.
I don't quite understand your pre_proccess Stage0. The result in paraview are difficut to guess. are you requesting Material assignment on faces?

Could you explain a bit.
Attaching modified command file for stage_1_load here:
Regards
Anirudh