FEM foundation B: heat transfer and thermal stress (solids, 2D, explicit), coupled temperature–displacement, solve.heat (#45)

* Heat transfer and thermal stress: thermal materials, temperature BCs, heat loads, heat transfer and coupled temperature–displacement steps, solve.heat

Model: Material.thermal (conductivity, specific heat, expansion, isotropic or
per axis; reference temperature), BoundaryCondition::Temperature (dof 11),
loads SurfaceFlux, Convection, HeatSource and Temperature (a field in static
steps), procedures HeatTransfer { transient (θ-method) } and
CoupledTemperatureDisplacement; checks for missing conductivity/specific
heat/expansion. fem: heat conduction kernels (conductivity, capacity,
source, face flux/film, heat flux) on the DofLayout (one T per node), thermal
strain load and stress D(ε − ε_th) for every solid formulation incl.
incompatible modes. Solver: steady and transient heat transfer, thermal loads
in static steps, coupled steps (exact one-way coupling). Engine: solve.heat,
temperature/heat-flux result fields, probes. Decks refuse heat transfer by
name. Analytic verification: slab, source+convection/flux, thick cylinder,
erfc semi-infinite solid, free/constrained expansion, bimetal strip, coupled
step.

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

* thermal: strains in 2D elements and explicit dynamics

Plane::thermal_load and stresses_with for plane stress (εzz free), plane
strain (σzz = −D₃·ε_th) and axisymmetric elements, incompatible modes
included; the solver's 2D kernels take them. Explicit dynamics turns a
step's temperature loads into a per-element thermal strain rate (reached
linearly over the step) subtracted from each strain increment, so it feeds
J2 and Johnson–Cook updates. Verified: free expansion in every 2D theory
and element, a biaxially held plate, an explicit free bar (ΔL = αΔT L,
stress-free) and a clamped bar at −EαΔT, capped at the yield stress with
perfect plasticity.

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

* clippy

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

* thermal: trusses take the axial thermal strain; keep the roadmap's M7 line

Truss::thermal_load and stresses_with project the thermal strain on the
member's tangent (Σ αₖ tₖ² ΔT); the static solver applies them to rod2/rod3
(#38). Explicit trusses take none yet and a warning says so.

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

---------

Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

crates/explicit/src/elements.rs

@@ -311,6 +311,17 @@ fn update(mat: &Material, es: &mut ElementState, q: &Mat3, d: &[f64; 6], vol: f6
     }
 }
 
+/// The mechanical part of a strain increment: less the thermal strain increment `thermal` in
+/// every normal direction (isotropic expansion, the same in any frame).
+fn mechanical(mut d: [f64; 6], thermal: f64) -> [f64; 6] {
+    if thermal != 0.0 {
+        for x in d.iter_mut().take(3) {
+            *x -= thermal;
+        }
+    }
+    d
+}
+
 /// The density and dilatational wave speed of an element of rest volume `rest`, now of volume
 /// `volume`.
 fn current(mat: &Material, rest: f64, volume: f64) -> (f64, f64) {
@@ -386,6 +397,7 @@ pub fn internal_forces(sys: &System, m: &Motion, state: &mut State, ws: &mut Wor
         let g = mid.gradient(&e.du);
         let q = rotation_of(sys, mat, es, &g, h.label, m.time)?;
         let (d, _) = rotation::split(&g);
+        let d = mechanical(d, h.thermal_rate * m.dt);
         let (rho, c) = current(mat, h.kinematics.volume, now.volume);
         update(mat, es, &q, &d, d[0] + d[1] + d[2], m.dt, rho, mid.volume);
         if let Some(failure) = es.failed {
@@ -466,8 +478,10 @@ pub fn internal_forces(sys: &System, m: &Motion, state: &mut State, ws: &mut Wor
             let averaged = t.nodes.iter().map(|n| ws.theta.get(*n).copied().unwrap_or(0.0)).sum::<f64>() / 4.0;
             let q = rotation_of(sys, mat, es, &inc.g, t.label, m.time)?;
             let (d, _) = rotation::split(&inc.g);
+            let thermal = t.thermal_rate * m.dt;
+            let d = mechanical(d, thermal);
             let (rho, c) = current(mat, t.kinematics.volume, inc.now.volume);
-            update(mat, es, &q, &d, averaged, m.dt, rho, inc.mid.volume);
+            update(mat, es, &q, &d, averaged - 3.0 * thermal, m.dt, rho, inc.mid.volume);
             if let Some(failure) = es.failed {
                 state.eroded.push((t.index, failure));
                 continue;