Apologies for my misunderstanding about the Eulerian domain in 2D (and thanks for teaching me this fact ). You are right, I just checked the document that even in the newer version these Eulerian domain controls are not available for 2D. (Sorry I got a wrong impression by looking at the Mechanical interface and saw the Eulerian domain in "Analysis Settings", shown below)
This may not apply to your case, but would it be possible if you can make it 3D by creating a small thickness, then only assign one layer of elements in the thickness direction, and constrain all the elements' z-DOF (It's like make it a plane-strain equivalent scenario)? By creating a 3D model with plane strain settings and only one layer of elements, you can still use your formulation in 2D and not significantly increase the number of nodes.
About the contact problem, I guess you are using trajectory-based contact detection in body interaction? You can find a description of the method if you search "body interactions in explicit dynamics analyses" (attached below, if you have trouble viewing the image, you can refer to the tip in this post:https://forum.ansys.com/forums/topic/retrieving-full-resolution-images-from-posts/). I would try reducing the time step size to see if it helps. My feeling is that it may miss a contact due to too high of velocity or something, then all the elements behind it will miss because these elements have not formed an open surface yet. I would also try making the mesh size in two bodies relatively similar to improve accuracy. Moreover, since you are still in the debugging process, I would suggest not use that fine mesh to reduce the pain of waiting.
About the Johnson-Cook material model, I wish I have more insights but I am not familiar with that material model. However, the fact that your Aluminum model is working gives a big hope. Maybe if you continue tweaking with the material parameters it can work for the Titanium too, or at least find out the root cause of the problem.