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/engine/src/cmd/define.rs

@@ -266,7 +266,7 @@ fn fluid_boundary(s: &mut Session, p: &Value) -> Result<Value> {
 pub const STEP_CREATE: CommandSpec = CommandSpec {
     id: "model.step.create",
     label: "New Step",
-    params: r#"{"name": "Bend", "procedure": {"type": "static"} | {"type": "nonlinear_static", "nonlinear_geometry": true, "initial_increment": 0.1, "min_increment": 1e-5, "max_increment": 1.0 (fractions of the step), "max_increments": 100, "max_iterations": 16 (per increment), "tolerances": {"force": 1e-6, "displacement": 1e-5, "energy": 1e-10}, "line_search": false, "load_path": [[0, 0], [0.5, 1], [1, 0]] (optional: the load factor against the step fraction, piecewise linear from [0, 0] to fraction 1; increments end at its points)} (loads and prescribed displacements are the load factor times their values; it ramps from 0 to 1 without a load path) | {"type": "frequency", "modes": 10, "min_hz": 0, "max_hz": 500} | {"type": "fluid", "domain": "Flow", "end_time": 1.0 | "steps": 1000, "time_step": (default: chosen for Mach 0.087 and τ ≤ 1), "frames": 10, "magic": 0.1875 (the two-relaxation-time Λ)} | {"type": "explicit_dynamic", "end_time": 0.001, "dt_scale": 0.9, "max_increments": 10000000, "output_interval", "history_interval", "history_nodes": "set", "initial_velocities": [{"set", "velocity": [vx, vy, vz]}], "rigid_walls": [{"set", "point", "normal"}], "hourglass": {"type": "viscous|stiffness", "coefficient": 0.1}, "bulk_viscosity": {"linear": 0.06, "quadratic": 1.5}}, "output": ["displacement", "reaction_force", "stress", "strain"] (default by procedure), "boundary_conditions": [names], "loads": [names] (active in this step; nothing carries over between steps), "before": "step" (default: last)}"#,
+    params: r#"{"name": "Bend", "procedure": {"type": "static"} | {"type": "nonlinear_static", "nonlinear_geometry": true, "initial_increment": 0.1, "min_increment": 1e-5, "max_increment": 1.0 (fractions of the step), "max_increments": 100, "max_iterations": 16 (per increment), "tolerances": {"force": 1e-6, "displacement": 1e-5, "energy": 1e-10}, "line_search": false, "load_path": [[0, 0], [0.5, 1], [1, 0]] (optional: the load factor against the step fraction, piecewise linear from [0, 0] to fraction 1; increments end at its points)} (loads and prescribed displacements are the load factor times their values; it ramps from 0 to 1 without a load path) | {"type": "frequency", "modes": 10, "min_hz": 0, "max_hz": 500} | {"type": "fluid", "domain": "Flow", "end_time": 1.0 | "steps": 1000, "time_step": (default: chosen for Mach 0.087 and τ ≤ 1), "frames": 10, "magic": 0.1875 (the two-relaxation-time Λ)} | {"type": "explicit_dynamic", "end_time": 0.001, "dt_scale": 0.9, "max_increments": 10000000, "output_interval", "history_interval", "history_nodes": "set", "initial_velocities": [{"set", "velocity": [vx, vy, vz]}], "rigid_walls": [{"set", "point", "normal", "friction": {"static": 0.3, "kinetic": 0.2, "decay": 10} (Coulomb; default frictionless)}], "hourglass": {"type": "viscous|stiffness", "coefficient": 0.1}, "bulk_viscosity": {"linear": 0.06, "quadratic": 1.5}}, "output": ["displacement", "reaction_force", "stress", "strain"] (default by procedure), "boundary_conditions": [names], "loads": [names] (active in this step; nothing carries over between steps), "before": "step" (default: last)}"#,
     kind: CommandKind::Model,
     run: step_create,
 };

crates/engine/src/cmd/solve.rs

@@ -58,7 +58,7 @@ pub const FREQUENCY: CommandSpec = CommandSpec {
 pub const EXPLICIT: CommandSpec = CommandSpec {
     id: "solve.explicit",
     label: "Solve Explicit Dynamic Step",
-    params: r#"{"step": "Impact", "max_dofs": 6000000, "max_increments": 1000000000, "max_output_values": 50000000, "threads": 8} — transient response of an explicit dynamic step (the only one when `step` is left out) by central differences; keeps its histories and field frames in the session; the caps may only be lowered (the step's own increment cap applies too); `threads` as for solve.static"#,
+    params: r#"{"step": "Impact", "max_dofs": 6000000, "max_increments": 1000000000, "max_output_values": 50000000, "max_contact_faces": 10000000, "threads": 8} — transient response of an explicit dynamic step (the only one when `step` is left out) by central differences, with the model's contacts (interaction.contact.*) and the step's rigid walls; keeps its histories and field frames in the session and reports each contact's peak force, first and last contact, deepest penetration, friction dissipated and the nodes adjusted at the start; the caps may only be lowered (the step's own increment cap applies too); `threads` as for solve.static"#,
     kind: CommandKind::Model,
     run: run_explicit,
 };
@@ -66,7 +66,7 @@ pub const EXPLICIT: CommandSpec = CommandSpec {
 pub const HISTORY: CommandSpec = CommandSpec {
     id: "solve.history",
     label: "Result Histories",
-    params: r#"{"step": "Impact", "every": 1} — the time histories of a solved explicit step: time, increment, energies, momentum, constraint force and the history nodes' displacement and velocity; `every` keeps one sample in so many (by default enough to return at most 10000)"#,
+    params: r#"{"step": "Impact", "every": 1} — the time histories of a solved explicit step: time, increment, energies, momentum, constraint force, the normal force across each contact (in `contacts` order) and the history nodes' displacement and velocity; `every` keeps one sample in so many (by default enough to return at most 10000)"#,
     kind: CommandKind::Model,
     run: history,
 };
@@ -289,6 +289,7 @@ fn run_explicit(s: &mut Session, p: &Value) -> Result<Value> {
         max_dofs: cap(p, "max_dofs", ExplicitLimits::MAX_DOFS)?,
         max_increments: cap(p, "max_increments", ExplicitLimits::MAX_INCREMENTS)?,
         max_output_values: cap(p, "max_output_values", ExplicitLimits::MAX_OUTPUT_VALUES)?,
+        max_contact_faces: cap(p, "max_contact_faces", ExplicitLimits::MAX_CONTACT_FACES)?,
     };
     let step = opt::<String>(p, "step")?;
     let model = &s.model;
@@ -314,6 +315,7 @@ fn explicit_summary(r: &ExplicitResult) -> Value {
         "frames": r.frames.len(),
         "history_samples": r.history.time.len(),
         "eroded": r.eroded,
+        "contacts": r.contacts,
         "warnings": r.warnings,
     })
 }
@@ -355,6 +357,8 @@ fn history(s: &mut Session, p: &Value) -> Result<Value> {
         "energies": pick(&|i| json!(h.energies.get(i))),
         "momentum": pick(&|i| json!(h.momentum.get(i))),
         "constraint_force": pick(&|i| json!(h.constraint_force.get(i))),
+        "contact_force": pick(&|i| json!(h.contact_force.get(i))),
+        "contacts": r.contacts.iter().map(|c| c.name.as_str()).collect::<Vec<_>>(),
         "nodes": nodes,
     }))
 }