Mesh configuration for multibody problem

Hello fenics communtity!

I am using fenics to solve the equations that describe the evolution of a rod in space. In my current code the rod is descritized by the centerline and after that I map it to the 3-dimensional space. The problem is 3dimensional. Now, I want to add a second rod, at a distance from the first one, that will follow the same evolution equations (with slightly different paramenters). At some point this rods will come in contact and I want to study their interaction too, that will have different evolution equations.

My question is very basic, but I am quite not a pro with very involved simulations. How should I set up the meshes for such a problem? Do I need to have a 3d box mesh and inside the 1d meshes for the the rods?