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/engine/src/lib.rs

@@ -428,6 +428,22 @@ mod tests {
             json!({"name": "A", "procedure": {"type": "fluid", "domain": "A", "end_time": -1, "steps": 3}}),
             json!({"name": "Bend", "procedure": {"type": "fluid", "domain": "nope", "end_time": 1}}),
             json!({"step": "Bend", "max_cells": 1e300, "max_steps": -3}),
+            // Heat transfer.
+            json!({"name": "A", "thermal": {"conductivity": -1}}),
+            json!({"name": "A", "thermal": {"conductivity": [1e308, f64::MIN_POSITIVE, 0]}, "density": 1}),
+            json!({"name": "A", "thermal": {"conductivity": "hot", "specific_heat": 0, "expansion": [1, 2]}}),
+            json!({"name": "A", "thermal": {}}),
+            json!({"name": "A", "thermal": {"expansion": 1e308, "reference_temperature": -1e308}}),
+            json!({"name": "A", "type": "temperature", "target": {"reference_point": "RP"}, "value": 1}),
+            json!({"name": "A", "type": "temperature", "target": {"set": "root"}, "value": "warm"}),
+            json!({"name": "A", "type": "surface_flux", "set": "end", "flux": 0}),
+            json!({"name": "A", "type": "convection", "set": "end", "film": -1, "sink": 1e308}),
+            json!({"name": "A", "type": "heat_source", "set": "all", "power": -1e308}),
+            json!({"name": "A", "procedure": {"type": "heat_transfer", "transient": {"end_time": 1e308, "increment": 1e-308}}}),
+            json!({"name": "A", "procedure": {"type": "heat_transfer", "transient": {"end_time": 1, "increment": 0.1, "theta": 0.1}}}),
+            json!({"name": "A", "procedure": {"type": "heat_transfer", "transient": {"end_time": -1, "increment": 0}}}),
+            json!({"name": "A", "procedure": {"type": "coupled_temperature_displacement", "extra": 1}}),
+            json!({"step": "Heat", "frame": u64::MAX, "nodes": [1]}),
             json!({"geometry": {"body": "Bar"}, "elements": [1, 99], "faces": [{"element": 1, "face": 200}]}),
             json!({"geometry": {"body": "Bar", "vertex": "v"}, "nodes": [1], "edges": [{"element": 1, "edge": 0}]}),
         ];