explicit: deformable contact and friction, verified by bars, sliding blocks, the patch test and Hertz

Segment-to-segment penalty contact between element faces: each secondary
face and each main face facing it are projected onto the secondary face's
plane, split into triangles, clipped (Sutherland–Hodgman) and integrated
with a three-point rule per sub-triangle (Puso–Laursen segmentation, the
penalty at the integration points as Fischer–Wriggers), so a uniform
pressure gives the consistent nodal forces on both meshes and the contact
patch test passes on non-matching meshes. Every contact runs both ways at
half the penalty: pairs with each surface as the secondary, general and
self contact face against face. A bucket grid of face boxes every
increment, faces integrated in parallel and their forces added in face
order: the same numbers on any thread count.

The penalty per area ε = s γ min(m/A)/Δt² comes from the lumped masses,
each node's directional area and the stable increment, bounded by
Gershgorin's row sums so contact never shortens the increment. Coulomb
friction with exponential decay by a regularised return map at the
secondary nodes; rigid walls take Coulomb impulses. Contact work and
friction dissipation join the energy balance; each contact reports its
peak force, first and last contact, deepest penetration, friction and the
nodes adjusted at the start (initial penetrations adjusted strain-free or
refused with the node, face and depth); a cap on contact faces.

Verified (crates/explicit/tests/contact.rs, tests/oracle/explicit-*):
colliding bars (2L/c +1.2%, ρcAv₀/2, KE kept to 0.005%, contact energy
back to 8e-5 of it), blocks sliding to a stop on a rigid wall and on a
plate under constant and decaying friction (0.005–0.2%), the patch test
(σ_zz uniform to 0.06%), two spheres colliding against Hertz (peak +2.3%,
duration −0.4%; the oracle case waits for a graded sphere mesher), a free
body untouched by general contact, determinism across threads. Oracle
measures gain `over` (ratios). Existing fixtures do not move.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

tests/oracle/explicit-sliding-block-contact/expected.json

@@ -0,0 +1,15 @@
+{
+ "title": "Block sliding to a stop on a deformable plate, friction decaying with the slip rate (explicit contact)",
+ "kind": "theory",
+ "source": "A rigid block launched at v₀ with friction μ(v) = μk + (μs − μk) e^(−d v) decelerates at g μ(v); it travels ∫₀^v₀ v dv / (g μ(v)) (Simpson's rule, 200 000 intervals) and stops after [v₀ + ln((μk + (μs − μk) e^(−d v₀))/μs)/d]/(g μk) = 1.2001; Meriam & Kraige, Engineering Mechanics: Dynamics, §3/5; the exponential decay law as in Oden & Martins, CMAME 52:527–634, 1985",
+ "quantities": [
+  {"id": "distance", "quantity": "distance travelled (top centre node) against ∫ v dv / (g μ(v)) = 2.01524",
+   "measure": {"command": "solve.probe", "params": {"step": "Slide", "at": [[0.5, 0.5, 0.5]]}, "pointer": "/nodes/0/displacement/0"},
+   "value": 2.015240387808855, "tolerance": {"relative": 0.01},
+   "reason": "the block bounces on the penalty springs and the plate under it shears elastically, so the normal force and the slip rate it feels vary by a little around their rigid-body values"},
+  {"id": "velocity", "quantity": "velocity of the top centre node after the stop",
+   "measure": {"command": "solve.probe", "params": {"step": "Slide", "at": [[0.5, 0.5, 0.5]]}, "pointer": "/nodes/0/velocity/0"},
+   "value": 0.0, "tolerance": {"absolute": 0.03},
+   "reason": "the block sticks; what is left is its elastic vibration, under 1% of v₀"}
+ ]
+}