Hi Martin,
Finite viscoelasticity is a highly nontrivial problem. The simple solve syntactic sugar won’t work (I assume you would have figured that out already). It does, however, work for some simple meshes. A POC is here (FEniCS_Shrimali_Ghosh_Kumar_Lopez-Pamies/viscoFEM.py at main · bhaveshshrimali/FEniCS_Shrimali_Ghosh_Kumar_Lopez-Pamies · GitHub) in case if you are interested. The code isn’t super well documented, but I would be happy to help with any questions if you have.
For real problems, with more intricate meshes I would recommend designing your own solver using either of NewtonSolver or PETScSNESSolver classes or using petsc4py directly.