verification: hyperelastic and thermal oracle cases and documentation

Five cases against closed forms: a Mooney-Rivlin block in Treloar's
uniaxial, equibiaxial and pure-shear modes and a Yeoh block in uniaxial
tension (the compressible energy's stresses, exact); a stretched
Mooney-Rivlin tube inflated by a follower pressure (Rivlin's incompressible
solution, 0.6 % at nu = 0.4995); free and fully held thermal expansion at a
thermal stretch of 1.2 (exact); a bar held at its ends heated past yield
(exact). docs/fem.md, the literature, ROADMAP (M15, M17), parity and the
oracle page follow.

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

tests/oracle/j2-heated-bar/README.md

@@ -0,0 +1,8 @@
+# A heated bar held at its ends past yield
+
+A steel bar 4 × 1 × 1 of 4 hex8 elements (E = 200000, ν = 0.3, σ_y = 250, H = 2000 isotropic,
+α = 1.2·10⁻⁵ from 20 degrees) on symmetry planes at x = 0, y = 0, z = 0 and held at x = 4 (its
+axial strain is zero; the lateral faces are free), heated uniformly to 320 by a temperature load
+in a nonlinear static step without nonlinear geometry. The mechanical strain is −α ΔT = −0.0036,
+2.9 times the yield strain, so the bar yields in compression: σ = −(σ_y + E_t (α ΔT − σ_y/E)) =
+−254.653 with E_t = E H/(E + H), and ε_p = (|σ| − σ_y)/H.

tests/oracle/j2-heated-bar/expected.json

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+{
+ "title": "A steel bar held at its ends and heated past yield (small strain)",
+ "kind": "theory",
+ "source": "Uniaxial J2 plasticity with linear hardening (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) with the additive thermal strain: the bar's total axial strain is held at zero, so its mechanical strain is −α ΔT and σ = −(σ_y + E_t (α ΔT − σ_y/E)) once α ΔT exceeds σ_y/E",
+ "quantities": [
+  {
+   "id": "sigma",
+   "quantity": "axial stress, ΔT = 300 (α ΔT = 3.6·10⁻³, 2.9 times the yield strain)",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Heat",
+     "elements": [
+      2
+     ]
+    },
+    "pointer": "/elements/0/stress/0/0"
+   },
+   "value": -254.65346534653466,
+   "tolerance": {
+    "relative": 1e-08
+   },
+   "reason": "a homogeneous uniaxial state the elements represent exactly"
+  },
+  {
+   "id": "plastic_strain",
+   "quantity": "equivalent plastic strain",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Heat",
+     "elements": [
+      2
+     ]
+    },
+    "pointer": "/elements/0/plastic_strain/0"
+   },
+   "value": 0.0023267326732673297,
+   "tolerance": {
+    "relative": 1e-07
+   },
+   "reason": "(|σ| − σ_y)/H, as for the stress"
+  }
+ ]
+}

tests/oracle/j2-heated-bar/fixture.json

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+{
+  "note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
+  "values": {
+    "plastic_strain": {
+      "band": 2.3267326732675587e-12,
+      "value": 0.0023267326732675587
+    },
+    "sigma": {
+      "band": 2.5465346534653467e-7,
+      "value": -254.6534653464418
+    }
+  }
+}

tests/oracle/j2-heated-bar/recipe.json

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+[
+ {"command": "mesh.block", "params": {"body": "Bar", "kind": "hex8", "corners": [[0, 0, 0], [4, 0, 0], [4, 1, 0], [0, 1, 0], [0, 0, 1], [4, 0, 1], [4, 1, 1], [0, 1, 1]], "divisions": [4, 1, 1], "faces": {"6": "x0", "3": "y0", "1": "z0", "4": "x1"}}},
+ {"command": "model.set.create", "params": {"name": "all", "geometry": [{"body": "Bar"}]}},
+ {"command": "model.set.create", "params": {"name": "x0", "geometry": [{"body": "Bar", "face": "x0"}]}},
+ {"command": "model.set.create", "params": {"name": "y0", "geometry": [{"body": "Bar", "face": "y0"}]}},
+ {"command": "model.set.create", "params": {"name": "z0", "geometry": [{"body": "Bar", "face": "z0"}]}},
+ {"command": "model.set.create", "params": {"name": "x1", "geometry": [{"body": "Bar", "face": "x1"}]}},
+ {"command": "model.material.create", "params": {"name": "Steel", "elastic": {"type": "isotropic", "young": 200000.0, "poisson": 0.3}, "plastic": {"type": "bilinear", "yield_stress": 250.0, "hardening_modulus": 2000.0}, "thermal": {"expansion": 1.2e-05, "reference_temperature": 20.0}}},
+ {"command": "model.section.create", "params": {"name": "bar", "set": "all", "material": "Steel", "kind": {"type": "solid"}}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sx0", "type": "symmetry", "target": {"set": "x0"}, "plane": "x"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sy0", "type": "symmetry", "target": {"set": "y0"}, "plane": "y"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sz0", "type": "symmetry", "target": {"set": "z0"}, "plane": "z"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sx1", "type": "symmetry", "target": {"set": "x1"}, "plane": "x"}},
+ {"command": "model.load.create", "params": {"name": "heat", "type": "temperature", "target": {"set": "all"}, "value": 320.0}},
+ {"command": "model.step.create", "params": {"name": "Heat", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false}, "boundary_conditions": ["sx0", "sy0", "sz0", "sx1"], "loads": ["heat"]}},
+ {"command": "solve.nonlinear", "params": {"step": "Heat"}, "id": "solve"}
+]