solver: mortar contact in nonlinear static steps

Frictionless contact pairs enforced by an augmented Lagrangian: nodal pressures from the
mortar weighted gaps, Uzawa updates after each converged increment until the gaps are within
1e-5 of the element thickness, and the consistent tangent (outer products of the weighted
gap gradients and the pressure-weighted Hessians from the automatic differentiation of the
mortar integrals). Finite sliding searches and integrates on the current configuration every
evaluation; without nonlinear geometry the pairs and their mortar integrals are fixed in the
reference configuration (small sliding, linear and exact). The tangent's pattern takes the
face pairs' blocks; the step cuts back when the active set chatters. Initial overclosure is
offset or refused; general contact, 2D models and arc length are refused by name; the linear
analyses refuse contact by name instead of the mesh.

With contact the convergence force scale comes from the converged states, the loads and the
current state. The loads-and-reactions balance check takes the nodal reactions into its scale
(no spurious warning for a part squeezed between held faces).

Tests: the contact patch test on non-matching hex8/tet4 meshes (exact with small sliding,
to 1e-4 with finite sliding), Hertz cylinder on a flat (peak pressure within 3%, half-width
bracketed) with quadratic Newton convergence, overclosure, thread-count determinism and the
refusals; Hertz sphere on a flat (heavy).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/solver/src/buckle.rs

@@ -113,6 +113,7 @@ pub fn solve_buckle(model: &Model, step: Option<&str>, limits: &Limits) -> Resul
     };
     step.procedure.validate()?;
     let resolved = model.resolve()?;
+    crate::system::refuse_contact(model, "buckling")?;
     let mesh = Mesh::new(model, &resolved, limits.max_dofs)?;
     if let Some(t) = mesh.trusses.first() {
         return Err(Error::NotSupported(format!(