If you created a large strain version of the input, try and convert it to use MOOSE's automatic differentiation system. A few places to look at:

Here is the converted input:

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    # we added this in the first exercise problem
    strain = FINITE
    # enable the use of automatic differentiation objects
    use_automatic_differentiation = true
  []
[]

[BCs]
  [bottom_x]
    # we use the AD version of this boundary condition here...
    type = ADDirichletBC
    variable = disp_x
    boundary = bottom
    value = 0
  []
  [bottom_y]
    # ...and here
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [Pressure]
    [top]
      boundary = top
      function = 1e7*t
      # make the action add AD versions of the boundary condition objects
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [elasticity]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
[]

[Executioner]
  type = Transient
  # MOOSE automatically sets up SMP/full=true with NEWTON
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]
(moose/modules/solid_mechanics/tutorials/introduction/mech_step02a.i)

Input file

SolidMechanics QuasiStatic Physics

Adding use_automatic_differentiation = true here causes the action to build the automatic differentiation (AD) enabled versions of the materials, kernels, and output objects it sets up.

BCs

We replaced DirichletBC with the AD-enabled ADDirichletBC object. Note that in general it is fine to mix AD and non-AD objects, although you might then end up with a less than perfect Jacobian. Also keep in mind that you cannot use AD and non-AD versions of material properties (such as the stiffness tensor or the strain) interchangeably. If an object requests an AD property you need to use the AD-enabled version of the material to provide it.

In the Pressure action we also supplied use_automatic_differentiation = true to have the action build the AD-enabled versions of the individual boundary condition objects that act on the displacement variables in the problem.

Materials

As mentioned above, when using AD-enabled kernels (added through the quasi static physics syntax), we must supply them with AD-enabled material properties. That's why we select the AD-enabled objects to compute stiffness tensor and stress. (The AD-enabled strain calculator is automatically added by the quasi-static physics.)

Note that in the first exercise we switched to a large strain formulation. In case you didn't make that change use ADComputeLinearElasticStress here and make sure you do not have strain = FINITE in the quasi-static physics.

Executioner

We select Newton as the solve type. MOOSE actually sets up the appropriate preconditioning block for us automatically in this case, which is why we removed it from the input file here.

What did you observe when you ran the converted example?

You should see a substantial reduction in linear iterations. This is an indication that the new Jacobian matrix generated by automatic differentiation is more accurate than the hand coded Jacobians in the non-AD version.

Rerun the problem again with a Young's modulus of 1e8.

Again each non-linear iteration converges with just two linear iterations, but the problem is still exhibiting a lot of non-linear steps and even some cut time steps due to the nonlinearity of the large deformation formulation.