Many thanks @dokken.
And in the case of inherent large deformation in which smoothing mesh is not sufficient? I mean, if I really need to compute collisions and anihilate them?

I’m not sure what you mean by collision management. If your mesh degenerates, you will still be able to solve the problem, but the quality of the solution will degenerate.

FEniCS expects that you send in sensible data, i.e. sensible meshes/geometries, valid boundary conditions etc.

Actually, I have a mesh which interpenetrates/autocollides, as illustrated below. In a real material, I would assume the mesh walls would compress themselves without interpenetrating, but here part of the mesh is just disappearing and that is what I would like to correct.

For now, I am trying to apply a “corrective” force F independently from the variational form (I assume then this force is “numerical” and not “physicial”). Here is the process: I solve the problem, get the deformation, apply deformation to the mesh and in case the new mesh is interpenetrating, I then apply the corrective force doing ALE.move(mesh, F), before going to next timestep.

My questions were actually associated to that issue:

Is there a specific way in FEniCS correct interpenetration of the mesh?

This is contact mechanics, and you would need to enforce the contact through your variational formulation, with either a Nitsche method or a penalty approach.