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

crates/explicit/src/elements.rs

@@ -70,6 +70,8 @@ pub struct Workspace {
     pub stress_force: Vec<f64>,
     pub hourglass_force: Vec<f64>,
     pub viscous_force: Vec<f64>,
+    /// Contact forces on the model per degree of freedom (empty without contact).
+    pub contact_force: Vec<f64>,
     /// Per node: the volume-weighted volumetric strain increments of its tetrahedra, and their
     /// volume.
     theta: Vec<f64>,
@@ -86,6 +88,7 @@ impl Workspace {
             stress_force: vec![0.0; dofs],
             hourglass_force: vec![0.0; dofs],
             viscous_force: vec![0.0; dofs],
+            contact_force: if sys.contacts.is_empty() { Vec::new() } else { vec![0.0; dofs] },
             theta: vec![0.0; n],
             tet_volume: vec![0.0; n],
             tet_increment: vec![None; sys.tets.len()],