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Smooth rigid contact and fixed-tool periodic MPC candidate — 2026-10-17

Status: source-level, experimental serial candidate. This note is not a release claim or a validation of general die forming.

Numerical and product contract

The Model continues to own one RigidContactPair. A solver-neutral contact Operator composes the existing boundary trace, current-pose projection and penalty point law. For a negative signed gap g, its reference-area penalty potential is k g²/2. The current-trial structural residual is the first variation; on a fixed smooth active branch, its Newton contribution is k(n ⊗ n + g ∇²g). Analytical spheres and cylinders supply the signed-gap Hessian, including the cylinder's current rotated axis. Triangular facets retain the previously reviewed planar-branch derivative and reject active free/noncoplanar edges. The surface is reprojected for every Newton and line-search trial; no old gap or force is reused.

The ordinary finite-strain J2 Step admits one such serial, frictionless tool with strong boundary conditions. The separate affine-periodic J2 Step admits one fixed tool. The Procedure assembles the complete material-plus-contact residual and tangent before TᵀR and TᵀKT; the same complete residual is used for the initial norm, every Newton update, line-search trial and periodic reaction. Material State retains trial/commit/rollback and accepted-increment checkpoint ownership. The fixed rigid tool owns no mutable pose state, so its coordinate work is exactly zero. Its boundary traction nevertheless makes a material-only Hill–Mandel report invalid; that output is rejected rather than silently reported.

Executable evidence

  • Sphere and cylinder, interior and exterior admissible sides: pointwise energy variation and full active-branch tangent agree with independent central differences. A rotated cylindrical axis is also covered.
  • On actual tetrahedral and hexahedral DOLFINx boundaries with CG1 and CG2 traces, sphere and cylinder penalty energy, assembled nodal residual and tangent action agree with a separate UFL potential differentiated by DOLFINx. This checks quadrature and DOF assembly, not only the local formula.
  • Ordinary public model.step(...) finite-J2 tetrahedral and hexahedral cases with a sphere or cylinder complete with active contact. A moving sphere also has a generalized tool force conjugate to the derivative of its penalty potential, and preserves accepted displacement, material state and pose after an injected energy failure.
  • The affine-periodic public Step has active fixed-sphere and fixed-triangle contact cases. The converged total residual is reduced below the tested tolerance. The projected contact tangent matches a finite difference of the projected contact residual. A partial fixed-tool solve saves and resumes to the uninterrupted displacement, material state and constraint-dual history. A changed tool is rejected by checkpoint identity. An injected projection or tangent-assembly failure after a partial solve restores the last accepted displacement, material and dual ledger; a subsequent retry continues. Moving periodic contact is rejected in capability discovery and Step construction.
  • A pure-Python candidate wheel includes all three new contact modules. An isolated installation of that wheel ran the public sphere example from outside the source checkout to a completed result with active contact. Both sphere and cylinder source-checkout examples also completed.

These are bounded local and small-global tests. No independent curved-tool structure benchmark, mesh/penalty/increment sensitivity study, full native installed-wheel release gate or remote CI is claimed here. One bounded two-rank admission group confirmed that standard and affine-periodic distributed implicit contact are rejected; this is not distributed numerical validation. The same geometry assumptions and tolerances must be checked for a real tool before promotion.

Next gates

  1. Validate a curved structural case against an independent reference and report force, moment, penetration, energy/work, mesh, penalty and increment sensitivity; do not use one visually plausible stress plot as the gate.
  2. Develop a reviewed transition rule for noncoplanar triangle seams, free edges and vertices, or use a genuinely smooth surface representation. Neither a zero curvature tensor at a crease nor silent normal averaging is an acceptable consistent tangent.
  3. Admit moving rigid tools with periodic MPC only after adding the accepted pose, tool work and rollback/restart evidence to the same affine lifecycle.
  4. Add owner/ghost residual and tangent assembly, distributed reactions and rank-portable restart before MPI implicit-contact admission. Friction and mixed displacement-pressure remain separate numerical gates.