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Moving rigid contact under affine-periodic J2 — source candidate

Status: experimental serial source candidate, not a release or general die-forming claim.

Ownership and numerical route

The Model still owns one RigidContactPair and one prescribed rigid motion. The affine Procedure owns the load coordinate and sets the current tool pose before every increment trial. The existing rigid-contact Operator recomputes projection at every Newton and line-search trial; the existing affine solver assembles material plus contact in full space before applying TᵀR and TᵀKT. No contact-specific Newton loop or alternative J2 material path was introduced.

At each accepted station, the provider publishes its work-conjugate tool force/moment and translation/rotation coordinate. A restartable accepted-path history integrates their trapezoidal work. Trial or failed-increment samples never enter this ledger. The Procedure restores pose, displacement, material state, affine and tool dual histories together after failure. Checkpoints bind the Operator identity and require the complete accepted tool path; loading a damaged or incomplete path is rejected atomically.

The work integral is a path-discretization record, not a claim of exact first- law closure for arbitrary plasticity and contact. The existing material-only Hill–Mandel result remains unavailable when contact is present.

Verified scope

  • One serial, frictionless sphere/cylinder or reviewed triangular rigid tool with normalized 0 → 1 prescribed motion; the triangle active branch must remain on smooth planar facets or coplanar seams.
  • The public model.step(...) affine-periodic J2 workflow completes with an active moving sphere, records tool work, and publishes a work-available constraint contract.
  • The endpoint generalized force agrees with an independent finite difference of the contact potential with respect to tool motion.
  • Partial-run checkpoint/restart matches uninterrupted displacement and tool force history. Injected projection failure restores displacement, committed material state, accepted factor, tool pose and both dual ledgers; retry succeeds.
  • Focused local FEniCSx/packaging regression: 125 passed, with the existing published-version identity test excluded; the separate two-rank rejection check passed 6 tests per rank on 2026-10-17. This is source-checkout evidence, not installed-wheel or remote-CI evidence for this follow-on.

Deliberate boundaries and next gate

Non-normalized physical-time tool schedules, multiple pairs, friction, mixed pressure, active free or noncoplanar triangle edges, and MPI implicit contact remain rejected. A general die surface needs either a reviewed smooth geometry with a differentiable signed gap or a feature-aware nonsmooth contact law; averaging adjacent facet normals while keeping the old gap is not a variationally consistent substitute. Before promotion, compare a curved structural problem against an independent reference and study mesh, penalty and increment sensitivity, then run installed-wheel and remote gates.

Smooth geometry extension: source candidate

The follow-on source change separates geometric differentiability from the penalty law. SmoothRigidSurface now supplies the current-pose projection and SurfaceGapDifferential; the latter binds the signed-gap Hessian to that exact projection, checks finiteness, symmetry, closest-point consistency and the signed-distance normal nullspace. A public, opt-in central-difference checker compares the gap gradient and Hessian at selected smooth points without adding finite differences to every Newton iteration. The plane, sphere and cylinder share this contract. A separate SmoothRigidSurface implementation can enter the same serial J2 model.step route without a new Step provider or contact law. The affine-periodic composition uses the same admission and Operator.

This is not a claim of arbitrary CAD contact. The geometry provider must guarantee a unique closest point on its declared valid branch and supply the Hessian of its own signed gap; one spot check cannot certify its entire domain. For a genuinely smooth CAD/parametric patch, projection and differential still need independent patch-transition validation. For a physically sharp closed feature, define its admissible side and feature-specific nonsmooth response explicitly, with branch changes handled by a tested semismooth or cutback procedure. Open trims and ambiguous projections remain rejected until their physical side and edge behavior are declared. Do not silently replace supplied geometry with normal averaging or a hidden fillet.

The focused follow-on check on 2026-10-17 passed 116 serial FEniCSx tests covering smooth and facet contact, standard and affine J2, geometry contracts, and rollback/restart. Six rank-sensitive tests skipped in that serial command then passed separately under two MPI ranks (6 per rank), confirming the unsupported distributed implicit-contact route still fails closed. An externally defined smooth plane was accepted by the public J2 Step; this tests the extension seam, not an independently validated CAD surface.

The first acceptance matrix should include smooth patch interiors and seams, noncoplanar edge and vertex crossings, opening/closing, independent energy directional differences, Newton residual/tangent differences, resultant force and moment, rejected-trial rollback, and mesh/penalty/increment sensitivity. Only then should a general imported curved die be admitted. The rationale is consistent with the closest-point solvability analysis and the smooth-geometry contact formulation; these references motivate the contract, not certify this implementation.