Phase 3b — Algorithmic tangent + Kuhn-Tucker lowering

[petlenz]

Part of the NumSim compiler epic: #28.

Summary

Generate algorithmic (consistent) tangents via implicit differentiation, and lower complementarity constraints (Kuhn-Tucker triples) into the LocalNewton residual via Fischer-Burmeister NCP functions. This is the highest schedule risk in the epic — de-risked by the Phase 1.3 spike.

Scope

3b.1 — AlgorithmicTangentPass

• For each output σ(x, ε):
  • dx/dε = −(∂R/∂x)⁻¹ · (∂R/∂ε) via implicit differentiation
  • dσ/dε = ∂σ/∂ε + ∂σ/∂x · dx/dε
• The rank-4 inverse is emitted as tmech::inv(...) per D7 — no Eigen runtime, no Voigt-flatten

3b.2 — KuhnTuckerLoweringPass

• ComplementarityConstraint(λ, f) → NCP Fischer-Burmeister: φ(λ, -f) = sqrt(λ² + f²) − (λ - f) = 0 inside the LocalNewton residual
• Non-smoothness at the kink handled by CAS's existing if_then_else-based piecewise differentiation (reuses Phase 3a's Newton solve; doesn't extend it)
• Multi-surface plasticity: multiple ComplementarityConstraints in one LNS

Acceptance

• J2 plasticity tangent matches FD within per-region tolerance at ~100 sampled strain points:
  • Tight (1e-6) in the smooth elastic + smooth plastic regimes
  • Looser (1e-4) through the elastic-plastic transition (FD is noisy at discontinuities)
• Drucker-Prager multi-surface recipe lowers and verifies
• Kinematic-hardening reverse loading verifies

Files affected

• New: include/numsim_codegen/passes/AlgorithmicTangentPass.h
• New: include/numsim_codegen/passes/KuhnTuckerLoweringPass.h
• Test recipes: tests/goldens/J2PlasticityFull.cpp (tangent now), tests/goldens/DruckerPrager.cpp

Dependencies

• Phase 3a — LocalNewtonLoweringPass is the consumer of KuhnTuckerLoweringPass's output

Risk

This is the highest-risk subissue in the epic. Schedule contingency: if the Phase 1.3 spike surfaces a fundamental issue with the implicit-diff approach, this gets re-scoped.