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/solvers/literature.md

@@ -1119,3 +1119,25 @@ update are written from (cited again in the module docs):
   and undeformed length of a flat-ended projectile). Published experimental Taylor-bar lengths
   (Wilkins & Guinan 1973) are not used: that needs the owner's sign-off for a tagged benchmark
   suite.
+
+## Part K: Heat transfer and thermal stress, as implemented
+
+- **Conduction.** Galerkin form of ρc Ṫ = ∇·(k∇T) + Q with surface flux and convection:
+  O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, *The Finite Element Method: Its Basis and
+  Fundamentals*, 7th ed., Butterworth-Heinemann 2013, §3.2; T. J. R. Hughes, *The Finite Element
+  Method*, Dover 2000, ch. 1. Kernels in `modelcraft_fem::heat`, solver in `modelcraft_solver::heat`.
+- **Time integration.** The generalized trapezoidal (θ) family, unconditionally stable for
+  θ ≥ ½ (Hughes 2000, §8.2): backward Euler (θ = 1, the default) and Crank–Nicolson (θ = ½).
+- **Thermal strain.** Initial-strain load ∫ Bᵀ D ε_th dV and stress D(ε − ε_th)
+  (Zienkiewicz, Taylor & Zhu 2013, §6.2.3); incompatible modes condensed with the same load.
+- **Coupled temperature–displacement.** One-way coupling (temperature strains the solid) solved
+  in turn, which is the exact monolithic solution of linear quasi-static thermoelasticity
+  without thermoelastic dissipation (B. A. Boley, J. H. Weiner, *Theory of Thermal Stresses*,
+  Wiley 1960, ch. 1).
+- **Verification** (`crates/solver/tests/thermal.rs`, analytic): steady slab conduction, a slab
+  with a heat source and convection or flux (quadratic profile), radial conduction through a
+  thick cylinder (T ∝ ln r), the semi-infinite solid T = erfc(x / 2√(κt)) (H. S. Carslaw,
+  J. C. Jaeger, *Conduction of Heat in Solids*, 2nd ed., Oxford 1959, §2.4), free and
+  constrained thermal expansion (σ = −EαΔT), the bimetal strip (S. Timoshenko, *Analysis of
+  bi-metal thermostats*, J. Opt. Soc. Am. 11(3):233–255, 1925), and the coupled step against
+  the heat step followed by the static step.