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Omar SobhandClaude Fable 5 6510045b5d rtx-fea: wire NonlinearStaticAnalysis — Newton on the consistent tangent, MMS-verified at second order
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NonlinearStaticAnalysis::run returned DVector::zeros unconditionally, like
ModalAnalysis and DynamicAnalysis before their repair. It is now full
Newton-Raphson on R(u) = f_ext - f_int(u):

- ElementMatrixComputer::compute_internal_force_and_tangent integrates
  f_int = int(B' sigma dV) and K_T = int(B' D_T B dV) in ONE quadrature
  sweep from a constitutive closure in the element's reduced Voigt space —
  computing both together is what keeps the tangent consistent with the
  stress, which is what quadratic convergence rides on.
- materials::reduced_constitutive bridges the Material trait (Voigt-6) to
  that closure: 3-D passes the total strain straight through; 2-D supports
  the linear plane-stress closed form and refuses nonlinear materials
  explicitly, since plane-stress condensation of a general law needs a
  per-point iteration that is not implemented yet.
- Dirichlet DOFs are held at their (load-scaled) values and Newton runs on
  the free DOFs, so the prescribed motion enters through f_int itself — no
  K_fc bookkeeping to get wrong. Body force enters via set_body_force, the
  same hook pattern the CFD solvers use for manufactured solutions. Uniform
  load stepping; other strategies and quasi-Newton refuse explicitly.
- StandardFiniteElement::compute_internal_forces, previously a zeros stub,
  now delegates to the same machinery.
- Mesh::validate is now called in run() (the old TODO), and NonlinearConfig
  gained a Default.

Verified two ways (tests/nonlinear_static.rs):

- Equivalence: with LinearElastic the loop lands on the directly assembled
  linear solution to 1e-10 in exactly one Newton step — same B, quadrature
  and solver, so any disagreement is the nonlinear assembly.
- Manufactured solution with a genuinely nonlinear material (energy
  W = 1/2 e'De + alpha/3 I1^3, so stress and tangent are exact derivatives;
  body force by central differences of the closed-form stress): L2 errors
  6.032e-2, 1.780e-2, 4.595e-3 on 2/4/8 Hex8 — observed orders 1.76 and
  1.95, climbing to the theoretical 2. The forcing contains the nonlinear
  term, so the order is reachable only if it is solved; an inconsistent
  tangent is caught separately by the iteration-count bound.

This unblocks ECSW model-order reduction, which needs a working nonlinear
solve underneath it. 551 rtx-fea tests, 0 failing.

Co-Authored-By: Claude Fable 5 <[email protected]>
2026-08-19 19:44:08 -07:00