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/j2-bauschinger/README.md

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+# Bauschinger effect of linear kinematic hardening
+
+One hex8 cube (E = 200000, ν = 0.3, σ_y = 250, H = 2000, Prager's linear kinematic hardening)
+held by symmetry on three faces, its fourth face pulled to a strain of 0.01 and brought back to
+zero within one nonlinear static step without nonlinear geometry, by the load path
+[[0, 0], [0.5, 1], [1, 0]] in increments of 0.05.
+
+At ε_a the stress is σ_a = σ_y + E_t (ε_a − σ_y/E) = 267.327. The yield surface keeps its size
+and moves with the back stress, so unloading is elastic only until σ_a − 2σ_y and then hardens
+with E_t: back at zero strain σ = σ_a − 2σ_y − E_t (ε_a − 2σ_y/E) = −247.525. Isotropic hardening
+would yield again only at −σ_a and end at −281.835. The equivalent plastic strain accumulates
+(σ_a − σ_y)/H forward and E/(E + H)(ε_a − 2σ_y/E) in reverse, 0.0160891.

tests/oracle/j2-bauschinger/expected.json

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+{
+ "title": "Bauschinger effect of linear kinematic hardening: tension, then back to zero strain",
+ "kind": "theory",
+ "source": "J2 plasticity with Prager's linear kinematic hardening in uniaxial stress (W. Prager, Ing.-Arch. 1955; Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3): from σ_a = σ_y + E_t (ε_a − σ_y/E) the material unloads elastically by 2σ_y and then hardens with E_t, so at zero strain σ = σ_a − 2σ_y − E_t (ε_a − 2σ_y/E)",
+ "quantities": [
+  {
+   "id": "residual_stress",
+   "quantity": "axial stress back at zero strain after a pull to ε_a = 0.01",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Pull",
+     "elements": [
+      1
+     ]
+    },
+    "pointer": "/elements/0/stress/0/0"
+   },
+   "value": -247.52475247524754,
+   "tolerance": {
+    "relative": 1e-06
+   },
+   "reason": "a homogeneous small-strain state the element represents exactly, with increments that end at the load path's turn; isotropic hardening would give −281.835 (it yields again only at −σ_a)"
+  },
+  {
+   "id": "plastic_strain",
+   "quantity": "accumulated equivalent plastic strain",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Pull",
+     "elements": [
+      1
+     ]
+    },
+    "pointer": "/elements/0/plastic_strain/0"
+   },
+   "value": 0.016089108910891083,
+   "tolerance": {
+    "relative": 1e-06
+   },
+   "reason": "(σ_a − σ_y)/H forward plus E/(E + H) (ε_a − 2σ_y/E) in reverse"
+  }
+ ]
+}

tests/oracle/j2-bauschinger/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": 1.6089108910891082e-11,
+      "value": 0.01608910891089074
+    },
+    "residual_stress": {
+      "band": 2.4752475247524754e-7,
+      "value": -247.52475247484173
+    }
+  }
+}

tests/oracle/j2-bauschinger/recipe.json

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+[
+ {"command": "mesh.block", "params": {"body": "Cube", "kind": "hex8", "corners": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1]], "divisions": [1, 1, 1], "faces": {"6": "x0", "3": "y0", "1": "z0", "4": "x1"}}},
+ {"command": "model.set.create", "params": {"name": "all", "geometry": [{"body": "Cube"}]}},
+ {"command": "model.set.create", "params": {"name": "x0", "geometry": [{"body": "Cube", "face": "x0"}]}},
+ {"command": "model.set.create", "params": {"name": "y0", "geometry": [{"body": "Cube", "face": "y0"}]}},
+ {"command": "model.set.create", "params": {"name": "z0", "geometry": [{"body": "Cube", "face": "z0"}]}},
+ {"command": "model.set.create", "params": {"name": "x1", "geometry": [{"body": "Cube", "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, "hardening": "kinematic"}}},
+ {"command": "model.section.create", "params": {"name": "cube", "set": "all", "material": "Steel", "kind": {"type": "solid"}}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sx", "type": "symmetry", "target": {"set": "x0"}, "plane": "x"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sy", "type": "symmetry", "target": {"set": "y0"}, "plane": "y"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "sz", "type": "symmetry", "target": {"set": "z0"}, "plane": "z"}},
+ {"command": "model.boundary_condition.create", "params": {"name": "pull", "type": "displacement", "target": {"set": "x1"}, "values": [0.01, null, null, null, null, null]}},
+ {"command": "model.step.create", "params": {"name": "Pull", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false, "initial_increment": 0.05, "max_increment": 0.05, "load_path": [[0, 0], [0.5, 1], [1, 0]]}, "boundary_conditions": ["sx", "sy", "sz", "pull"], "loads": []}},
+ {"command": "solve.nonlinear", "params": {"step": "Pull"}, "id": "solve"}
+]