fem, solver: thermal strain in nonlinear static steps

Temperatures now strain the material in nonlinear steps instead of being
refused. At finite strain the deformation gradient splits multiplicatively,
F = F_m F_theta with F_theta = diag(1 + alpha_i dT) at each point: the material
sees F_m and the loops run on the thermally expanded volume J_theta dV0 (mixed
elements project det F_m), so the tangent stays consistent. At small strain the
split is additive, and elements on their linear stiffness take the equivalent
nodal forces as a dead load. The step's temperatures are its temperature loads,
or the steady conduction of its temperature conditions and heat loads (one-way
coupling, as the linear coupled step); both at once are refused. They ramp with
the load factor from each material's reference temperature. Johnson-Cook
plasticity softens at the point's temperature. Verified: free expansion and a
fully constrained neo-Hookean block at 20 % thermal stretch, full and hybrid
(exact); a bar held at its ends heated past yield (exact); the linear limit and
the conducted temperatures against the linear solvers; tangents by central
differences with a temperature field.

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

crates/solver/src/analysis.rs

@@ -353,9 +353,9 @@ pub fn solve_static(model: &Model, step: Option<&str>, limits: &Limits) -> Resul
     // loads.
     let (field, temperature) = match step.procedure {
         Procedure::CoupledTemperatureDisplacement {} => {
-            let (labels, t) = crate::heat::temperatures(model, &resolved, step, limits)?;
-            let at = |l: &u32| labels.binary_search(l).ok().and_then(|i| t.get(i)).copied();
-            (Some(mesh.labels.iter().map(at).collect::<Vec<_>>()), Some(mesh.labels.iter().map(|l| at(l).unwrap_or(0.0)).collect()))
+            let field = crate::heat::temperatures_at(model, &resolved, step, limits, &mesh.labels)?;
+            let temperature = field.iter().map(|t| t.unwrap_or(0.0)).collect();
+            (Some(field), Some(temperature))
         }
         _ => (temperature_loads(model, &resolved, &mesh, step)?, None),
     };