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/nl-j2-uniaxial/README.md

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+# Uniaxial tension of a J2 bilinear-hardening cube to large strain (implicit)
+
+The cube of `j2-uniaxial-explicit` solved by the implicit nonlinear solver: one fully integrated
+hex8, E = 200000, ν = 0.3, σ_y = 250, H = 2000 (isotropic), held by symmetry on three faces and
+stretched on the fourth to λ = e^0.2 in a nonlinear static step, lateral faces free.
+
+Simo's exponential return map integrates this proportional path exactly in the logarithmic
+strain, so the Kirchhoff stress is the small-strain curve τ = σ_y + E_t (ε − σ_y/E) = 643.564 at
+ε = 0.2 and the equivalent plastic strain (τ − σ_y)/H = 0.196782. The Cauchy stress is
+σ = τ/J with Hencky's volume law ln J = τ/(3K): 642.737.
+
+Cross-check with the explicit solver: `j2-uniaxial-explicit` reaches 643.57 for the Cauchy stress
+with the same plastic strain. Its hypoelastic update takes the logarithmic strain rate against
+the Cauchy stress, while the implicit model is hyperelastic in the Kirchhoff stress: the two
+laws differ by the factor J = 1.0013 (the elastic volume change), which is the 0.13 % between
+them; both meet the closed form of their own law.

tests/oracle/nl-j2-uniaxial/expected.json

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+{
+ "title": "Uniaxial tension of a J2 bilinear-hardening cube to large strain (implicit, finite strain)",
+ "kind": "theory",
+ "source": "J2 plasticity with linear isotropic hardening in uniaxial stress (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) in the logarithmic strain, which Simo's exponential return map (CMAME 99:61–112, 1992) integrates exactly on a proportional path: Kirchhoff stress τ = σ_y + E_t (ε − σ_y/E), Cauchy stress σ = τ/J with ln J = τ/(3K) (Hencky's volume law)",
+ "quantities": [
+  {
+   "id": "sigma",
+   "quantity": "axial Cauchy stress at a logarithmic strain of 0.2",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Pull",
+     "elements": [
+      1
+     ]
+    },
+    "pointer": "/elements/0/stress/0/0"
+   },
+   "value": 642.7365391418857,
+   "tolerance": {
+    "relative": 1e-06
+   },
+   "reason": "a homogeneous deformation the element represents exactly, reached on a proportional path: the tolerance only admits the Newton tolerance and rounding"
+  },
+  {
+   "id": "plastic_strain",
+   "quantity": "equivalent plastic strain",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Pull",
+     "elements": [
+      1
+     ]
+    },
+    "pointer": "/elements/0/plastic_strain/0"
+   },
+   "value": 0.19678217821782182,
+   "tolerance": {
+    "relative": 1e-06
+   },
+   "reason": "ε_p = (τ − σ_y)/H, as for the stress"
+  }
+ ]
+}

tests/oracle/nl-j2-uniaxial/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": 1.9678217821795454e-10,
+      "value": 0.19678217821795452
+    },
+    "sigma": {
+      "band": 6.427365391418857e-7,
+      "value": 642.7365390754569
+    }
+  }
+}

tests/oracle/nl-j2-uniaxial/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": "isotropic"}}},
+ {"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": [0.22140275816016985, null, null, null, null, null]}},
+ {"command": "model.step.create", "params": {"name": "Pull", "procedure": {"type": "nonlinear_static"}, "boundary_conditions": ["sx", "sy", "sz", "pull"], "loads": []}},
+ {"command": "solve.nonlinear", "params": {"step": "Pull"}, "id": "solve"}
+]