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Nonlinear mechanics overview

This page explains the nonlinear architecture retained in QF Solver 0.2.11. It is a mechanics guide, not a verification report or a qualification decision. The 0.2.10 V&V summary explains what evidence exists and what it does not establish.

Assembly and Newton iteration

For a nonlinear equilibrium problem, the analysis evaluates an equilibrium residual and a consistent route-specific tangent at the current trial state. The Newton driver solves a correction equation, applies the selected update policy, and evaluates convergence/stagnation diagnostics. A common composite assembly interface can combine material, geometric, and contact contributions where a route implements them. It does not imply that every contribution is available for every element or analysis.

Public API / CLI
  -> AnalysisRouter
  -> nonlinear analysis and driver
  -> continuation / robustness policy
  -> NonlinearStateTransaction
  -> CompositeNonlinearAssembly
       -> material response
       -> geometric response (selected routes)
       -> contact response (selected routes)
  -> residual + tangent
  -> Newton correction and convergence decision

The residual/tangent interface gives the driver a consistent way to request assembly and diagnostics. Some contact active-set/recovery paths and the arc-length correction remain specialized; this is not a claim that the nonlinear implementation has no route-specific architecture.

Accepted and trial state

Path-dependent analyses must not mutate the accepted history while merely testing a Newton correction. The transaction model therefore distinguishes:

  1. Accepted state — the last converged state and material history.
  2. Trial state — a temporary evaluation for the current increment/iteration.
  3. Commit — accept the trial state after the route's convergence checks.
  4. Rollback — discard rejected trial changes before a cutback or retry.

Selected schema-v2 checkpoint routes can serialize and restore state for restart/replay. State digests are recorded where supported to help detect unexpected changes. The exact support depends on the route; do not infer frictional-contact, distributed, or nonlinear-dynamics restart support from the existence of the shared transaction primitives.

Continuation and robustness policies

The implementation includes Full Newton, line-search support, stagnation classification, handling for a numerical residual floor, adaptive increment control with cutback/retry, and a specialized arc-length route. These are robustness mechanisms, not proof that all nonlinear problems converge. The recorded arc-length scope does not establish general bifurcation or postbuckling tracking.

Route boundaries

  • Small-strain J2: use only the element-analysis combinations in the published 0.2.8 registry and their bounded decisions.
  • Corotational J2: allows large rotations while retaining a small-local- strain assumption; the formal bounded acceptance is the documented HEX8 route, not general finite-strain plasticity.
  • Total-Lagrangian geometry: a St. Venant–Kirchhoff campaign was audited for selected static serial TET4/HEX8 cases. Its audit says GO_WITH_LIMITATIONS and explicitly records no maturity promotion.
  • Contact: frictionless penalty contact remains experimental. Frictional stick/slip evidence is narrow and current-source formal requalification is not established.
  • Distributed execution: recorded two-rank PETSc/MPI evidence is bounded to selected linear-static cases; general nonlinear distributed assembly is not validated.

See known limitations before choosing a route.