Add backtracking to ElementJacobianDamper

[Andreas-Lepak]

refs #32806

Reason

ElementJacobianDamper already limits large element Jacobian changes on the displaced mesh, but
its probe path can still encounter a degenerate map when the full trial Newton update inverts an
element. In that case the solve falls back to a timestep cutback instead of trying a smaller
nonlinear update first.

This change adds an opt-in backtracking mode so the damper can reduce the probed update before FE
assembly reaches a DegenerateMap.

Design

• Add optional use_backtracking, backtrack_factor, and max_backtrack_steps parameters to
  ElementJacobianDamper.
• Refactor the damper probe into a helper that tests a damped trial update and reports the maximum
  relative JxW change.
• Treat degenerate-map exceptions during the probe as a signal that the trial damping is too large,
  then iteratively reduce the trial damping until the probe succeeds and the Jacobian increment is
  below max_increment.
• Always restore displaced node coordinates after a failed probe so the damper does not leave the
  displaced mesh in a modified state.
• Add a regression test covering the new backtracking path and update the damper documentation.

Impact

This is a backward-compatible enhancement to ElementJacobianDamper.

• Existing input files are unchanged unless they opt into use_backtracking = true.
• The new mode improves robustness for large-displacement solves that would otherwise fail probing a
  nonlinear update due to temporary element inversion.
• No existing APIs are removed or changed incompatibly.

Testing

• Ran exception_handling.i without backtracking to confirm the existing negative-Jacobian path is
  preserved.
• Ran exception_handling.i with Dampers/jac/use_backtracking=true to confirm the damper now
  reduces the update without emitting the negative-Jacobian error.
• Ran git diff --check.

[moosebuild]

Job Precheck, step Clang format on b97b5c9 wanted to post the following:

Your code requires style changes.

A patch was auto generated and copied here
You can directly apply the patch by running, in the top level of your repository:

curl -s https://mooseframework.inl.gov/docs/PRs/32807/clang_format/style.patch | git apply -v

Alternatively, with your repository up to date and in the top level of your repository:

git clang-format dba0fc8d126cb8a0d6b4e8eabf8b390a09e4aa91

[moosebuild]

Job Documentation, step Docs: sync website on 28794bd wanted to post the following:

View the site here

This comment will be updated on new commits.

[moosebuild]

Job Test, step Results summary on 28794bd wanted to post the following:

Framework test summary

Compared against a5a619e in job civet.inl.gov/job/3763732.

No change

Modules test summary

Compared against a5a619e in job civet.inl.gov/job/3763732.

Added tests

Test	Time (s)	Memory (MB)
solid_mechanics/test:jacobian_damper.backtrack_negative_jacobian	1.28	127.09

[moosebuild]

Job Coverage, step Generate coverage on 28794bd wanted to post the following:

Framework coverage

	a5a619	#32807 28794b
	Total	Total	+/-	New
Rate	85.88%	85.87%	-0.00%	-
Hits	132217	132216	-1	0
Misses	21747	21748	+1	0

Diff coverage report

Full coverage report

Modules coverage

Solid mechanics

	a5a619	#32807 28794b
	Total	Total	+/-	New
Rate	85.38%	85.37%	-0.01%	100.00%
Hits	28595	28643	+48	94
Misses	4896	4909	+13	0

Diff coverage report

Full coverage report

Full coverage reports

Reports

• framework
• chemical_reactions
• combined
• contact
• electromagnetics
• external_petsc_solver
• fluid_properties
• fsi
• functional_expansion_tools
• geochemistry
• heat_transfer
• level_set
• misc
• navier_stokes
• optimization
• peridynamics
• phase_field
• porous_flow
• ray_tracing
• rdg
• reactor
• scalar_transport
• solid_mechanics
• solid_properties
• stochastic_tools
• subchannel
• thermal_hydraulics
• xfem

This comment will be updated on new commits.