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 <[email protected]>
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 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* clippy

Co-Authored-By: Claude Opus 5.5 <[email protected]>
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 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

---------

Co-authored-by: jyviko <[email protected]>
Co-authored-by: Claude Opus 5.5 <[email protected]>

docs/fem.md

@@ -101,3 +101,35 @@ of the family's degree; on a curved map, linear fields exact with zero Hessian,
 physical Hessian of a quadratic interpolant consistent with finite differences of its physical
 gradient. The solver and explicit migration to `DofLayout` was checked bit for bit: every
 result of the solver, explicit, engine and io test suites hashes identically before and after.
+
+## Heat transfer and thermal strain
+
+A heat conduction element carries one temperature per node (`heat::HEAT_DOFS`, kind `T`);
+`heat::Conduction` gives the conductivity ∫ ∇Nᵀ k ∇N dV (full rule), the capacity ∫ ρc N Nᵀ dV
+and a source ∫ N Q dV (mass rule), and the heat flux −k∇T at the integration points;
+`heat::face_weights` and `face_film` integrate surface flux and convection on tri3/tri6/quad4/quad8
+faces. The solver (`modelcraft_solver::heat`) numbers the temperatures with
+`DofLayout::uniform(…, DofSet::TEMPERATURE)` and assembles with the same `sparse::add_block`.
+
+Thermal strain ε_th = α (T − T_ref) along the material axes enters a solid as the load
+`Solid::thermal_load(d, &ThermalStrain { alpha, delta })` = ∫ Bᵀ D ε_th dV and its stress as
+`Solid::stresses_with(d, u, Some(&thermal))` = D (ε − ε_th); `delta` is the nodal T − T_ref.
+2D elements have the same pair (`Plane::thermal_load`, `Plane::stresses_with`): plane stress
+leaves εzz free (σzz = 0), plane strain holds it (σzz = −D₃·ε_th), axisymmetric elements strain
+the hoop direction too. Trusses (rod2, rod3) take the axial part Σ αₖ tₖ² ΔT along their tangent (`Truss::thermal_load`,
+`Truss::stresses_with`). Shells and beams will provide the same two functions for their strains;
+springs, dashpots and point masses have no thermal strain.
+
+Explicit dynamics takes a step's temperature loads as a thermal strain rate per element,
+α ΔT / end time (the change reached linearly over the step, like a prescribed displacement, so
+there is no thermal shock), subtracted from each increment's strain increment before the
+constitutive update, so it feeds J2 and Johnson–Cook plasticity alike; isotropic expansion only
+(the rate is the same in any frame). Explicit trusses take no thermal strain yet (a warning
+says so).
+
+Model side: `Material::thermal` (`conductivity`, `specific_heat`, `expansion`, each isotropic
+or per axis, and `reference_temperature`), `BoundaryCondition::Temperature`, loads
+`SurfaceFlux`, `Convection`, `HeatSource` (heat transfer) and `Temperature` (a temperature field
+in a static step), procedures `HeatTransfer { transient }` and `CoupledTemperatureDisplacement`.
+Commands: `solve.heat`, and `solve.static` for coupled steps. The deck writers refuse heat
+transfer by name for now.