Newton Solver Does Not Converge in Mooney-Rivlin Hyperelasticity Example - Maximum Iterations Reached

Errors
3

To debug this, one should start with adding:

dolfinx.log.set_log_level(dolfinx.log.LogLevel.INFO)

which will give you info about the convergence:

[2024-12-03 20:50:59.115] [info] Column ghost size increased from 0 to 0
[2024-12-03 20:50:59.117] [info] PETSc Krylov solver starting to solve system.
[2024-12-03 20:50:59.118] [info] PETSc Krylov solver starting to solve system.
[2024-12-03 20:50:59.119] [info] Newton iteration 2: r (abs) = -nan (tol = 1e-08), r (rel) = -nan (tol = 1e-08)

Then, next I would change
solver.convergence_criterion = "incremental"
to
solver.convergence_criterion = "residual"
which gives:

[2024-12-03 20:51:46.479] [info] Column ghost size increased from 0 to 0
[2024-12-03 20:51:46.480] [info] Newton iteration 0: r (abs) = 35.740443828512376 (tol = 1e-08), r (rel) = inf (tol = 1e-08)
[2024-12-03 20:51:46.480] [info] PETSc Krylov solver starting to solve system.
[2024-12-03 20:51:46.481] [info] Newton iteration 1: r (abs) = -nan (tol = 1e-08), r (rel) = -nan (tol = 1e-08)

Next, I would modify the krylov solver for the underlying system, i.e.

solver.convergence_criterion = "residual"
solver.error_on_nonconvergence = False
from petsc4py import PETSc
ksp = solver.krylov_solver
options = {"ksp_type": "ksp", "pc_type": "lu", "pc_factor_mat_solver_type": "superlu",
           "ksp_error_if_not_converged": None, "ksp_monitor": None}
opts = PETSc.Options()
for key, val in options.items():
    opts.setValue(key, val)
ksp.setFromOptions()

However, I am not sure the variational form is correct, as

looks strange to me.
However, hyperelastic models is not my field of expertise.
There are other posts regarding Mooney-Rivlin at: Hyperelastic beam
which seems to use a very different variational formulation than you.
Similarly, see: 2D Hyper-elasticity — FEniCS solid tutorial 2019.0.2 documentation

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