Sebastian,
Use SpaceClaim to split the body instead of just the faces. You will end up with 4 bodies. On the Workbench tab, use the Share button. That will create shared topology. In Mechanical, select the ends to mesh first and they should automatically get a hex mesh. Then mesh the center body and it will get pyramid and tet elements that share nodes at the split planes. No contacts will be created.
You are navigating away from the AIS Discovery experience