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/decks/src/lsdyna/mod.rs

@@ -202,7 +202,7 @@ fn plan<'a>(model: &'a Model, r: &Resolved) -> Result<Plan<'a>> {
     let used: BTreeSet<&str> = model.sections().values().map(|s| s.material.as_str()).collect();
     let materials: BTreeMap<&str, u32> = used.into_iter().enumerate().map(|(i, m)| Ok((m, id(i)?))).collect::<Result<_>>()?;
     // Everything LS-DYNA cannot express, reported at once.
-    let mut refused = BTreeSet::new();
+    let mut refused = crate::thermal_items(model);
     let mut parts = Vec::new();
     let mut hourglasses: BTreeMap<Hourglass, u32> = BTreeMap::new();
     for (name, sec) in model.sections() {
@@ -311,6 +311,8 @@ fn plan<'a>(model: &'a Model, r: &Resolved) -> Result<Plan<'a>> {
                 Load::BodyForce { .. } => {
                     refused.insert(format!("load `{l}`: a body force per unit volume (LS-DYNA's body loads are accelerations; use gravity)"));
                 }
+                // In thermal_items.
+                Load::SurfaceFlux { .. } | Load::Convection { .. } | Load::HeatSource { .. } | Load::Temperature { .. } => {}
             }
         }
     }
@@ -818,8 +820,8 @@ fn write_step(d: &mut Deck, model: &Model, r: &Resolved, plan: &Plan, step: &Ste
                 d.card([Field::Blank, Field::Blank, Field::Blank, Field::Blank, Field::from(1)]);
             }
         }
-        Procedure::ExplicitDynamic(_) => {
-            return Err(Error::Unsupported { format: FORMAT, what: format!("step `{}`: explicit dynamic steps", step.name) });
+        Procedure::ExplicitDynamic(_) | Procedure::HeatTransfer { .. } | Procedure::CoupledTemperatureDisplacement {} => {
+            return Err(Error::Unsupported { format: FORMAT, what: format!("step `{}`: {} steps", step.name, step.procedure.name()) });
         }
     }
     d.line("*CONTROL_TERMINATION");
@@ -872,6 +874,9 @@ fn write_step(d: &mut Deck, model: &Model, r: &Resolved, plan: &Plan, step: &Ste
                 }
                 Load::BodyForce { .. } => return Err(broken(format!("load `{name}`: a body force"))),
                 Load::Centrifugal { .. } => return Err(broken(format!("load `{name}`: a centrifugal load"))),
+                Load::SurfaceFlux { .. } | Load::Convection { .. } | Load::HeatSource { .. } | Load::Temperature { .. } => {
+                    return Err(broken(format!("load `{name}`: a {} load", load.kind())));
+                }
             }
         }
         // The other concentrated loads node by node, summed where they share a node.