verification: implicit plasticity oracle cases and documentation

Four cases, each against its closed form: uniaxial tension of a J2 cube to a
logarithmic strain of 0.2 (Kirchhoff stress exact; 0.13 % from the explicit
solver's hypoelastic Cauchy stress, the elastic volume change between the two
laws), the Bauschinger effect of linear kinematic hardening on a load path
back to zero strain (exact), Hill's elastic-perfectly plastic thick cylinder
(bore displacement at a plastic radius of 1.5a within 0.009 %, collapse
pressure within 2e-8; the pending case is now active) and a cantilever's
plastic collapse, converged 3.1 % above beam theory's hinge, the bound a
continuum exceeds. docs/fem.md, the literature, ROADMAP (M15), 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/plastic-hinge-cantilever/README.md

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+# Plastic collapse of a cantilever
+
+A steel bar 200 long with a 10 × 10 section (E = 200000, ν = 0.3, elastic–perfectly plastic at
+σ_y = 250), reduced hex20 20 × 2 × 4, in a nonlinear static step without nonlinear geometry. The
+root x = 0 is a plane of symmetry (no rotation, the section free to contract laterally), held in
+Y, Z and against twist on average through a distributing coupling; a coupling at the tip pushes
+the end down by 15, 4.5 times the deflection at first yield.
+
+Beam theory's collapse is a plastic hinge at the root: M_p = σ_y b h²/4 = 62500 and
+P_c = M_p/L = 312.5. The solid's collapse lies above it, since a continuum cannot rotate about a
+hinge (that needs a jump of the normal velocity across the section): refined to 8 elements
+through the depth or 160 along the length, the force settles at 322.3, 3.1 % above. The case
+checks that the implicit plasticity reaches this plateau and holds it.

tests/oracle/plastic-hinge-cantilever/expected.json

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+{
+ "title": "Plastic collapse of a cantilever: the fully plastic moment at the root",
+ "kind": "theory",
+ "source": "Limit analysis (B. G. Neal, The Plastic Methods of Structural Analysis, 3rd ed., Chapman & Hall 1977, ch. 1–2): beam theory's plastic hinge at the root, the fully plastic moment M_p = σ_y b h²/4 of a rectangular section, collapses a cantilever of length L at P_c = M_p/L = 312.5 (b = h = 10, L = 200, σ_y = 250); a bound for the solid, whose collapse lies above it (W. Prager, P. G. Hodge, Theory of Perfectly Plastic Solids, Wiley 1951: a continuum mechanism allows no normal velocity jump, which the beam's hinge rotation is)",
+ "quantities": [
+  {
+   "id": "collapse_force",
+   "quantity": "tip force at a tip deflection of 15 (4.5 times the first yield's)",
+   "measure": {
+    "from": "solve",
+    "pointer": "/reference_points/1/reaction/2"
+   },
+   "value": -312.5,
+   "tolerance": {
+    "relative": 0.05
+   },
+   "reason": "the solid's collapse lies above beam theory's hinge: refined through the depth (4 to 8 elements) and along the length (40 to 160) the force settles 3.1 % above M_p/L (322.3), so the band is that bound's gap; the root is a symmetry plane (no rotation, free lateral contraction) held on average through a coupling, the tip pushed through another; reduced hex20, 20 × 2 × 4"
+  }
+ ]
+}

tests/oracle/plastic-hinge-cantilever/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": {
+    "collapse_force": {
+      "band": 3.2260685847425373e-7,
+      "value": -322.6068584742537
+    }
+  }
+}

tests/oracle/plastic-hinge-cantilever/recipe.json

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+[
+ {"command": "mesh.block", "params": {"body": "Beam", "kind": "hex20", "corners": [[0, 0, -5.0], [200.0, 0, -5.0], [200.0, 10.0, -5.0], [0, 10.0, -5.0], [0, 0, 5.0], [200.0, 0, 5.0], [200.0, 10.0, 5.0], [0, 10.0, 5.0]], "divisions": [20, 2, 4], "faces": {"6": "root", "4": "tip"}}},
+ {"command": "model.set.create", "params": {"name": "all", "geometry": [{"body": "Beam"}]}},
+ {"command": "model.set.create", "params": {"name": "root", "geometry": [{"body": "Beam", "face": "root"}]}},
+ {"command": "model.set.create", "params": {"name": "tip", "geometry": [{"body": "Beam", "face": "tip"}]}},
+ {"command": "model.material.create", "params": {"name": "Steel", "elastic": {"type": "isotropic", "young": 200000.0, "poisson": 0.3}, "plastic": {"type": "bilinear", "yield_stress": 250.0}}},
+ {"command": "model.section.create", "params": {"name": "beam", "set": "all", "material": "Steel", "kind": {"type": "solid"}, "formulation": {"integration": "reduced"}}},
+ {"command": "model.boundary_condition.create", "params": {"name": "plane", "type": "symmetry", "target": {"set": "root"}, "plane": "x"}},
+ {"command": "model.reference_point.create", "params": {"name": "Root", "xyz": [0, 5.0, 0]}},
+ {"command": "model.coupling.create", "params": {"name": "support", "reference_point": "Root", "set": "root", "kind": "distributing"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "hold", "type": "displacement", "target": {"reference_point": "Root"}, "values": [null, 0, 0, 0, null, null]}},
+ {"command": "model.reference_point.create", "params": {"name": "Tip", "xyz": [200.0, 5.0, 0]}},
+ {"command": "model.coupling.create", "params": {"name": "end", "reference_point": "Tip", "set": "tip", "kind": "distributing"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "push", "type": "displacement", "target": {"reference_point": "Tip"}, "values": [null, null, -15.0, null, null, null]}},
+ {"command": "model.step.create", "params": {"name": "Collapse", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false}, "boundary_conditions": ["plane", "hold", "push"], "loads": []}},
+ {"command": "solve.nonlinear", "params": {"step": "Collapse"}, "id": "solve"}
+]