verification: nonlinear oracle cases and the nonlinear solver's documentation

Theory cases for the nonlinear solver, each frozen as a fixture: uniaxial
stretch of a neo-Hookean block to twice its length (closed form), the
nonlinear patch test on a distorted hex8 mesh, a quarter turn of the same
mesh (objectivity: zero stress), the elastica of a hex20 cantilever at
P L²/(E I) = 1, 2, 5, 10 against Bisshopp–Drucker (0.2–0.5 %), and the
inflation of a thick neo-Hookean tube by a follower pressure against
Rivlin's closed form (0.08 % at the bore). A finite-strain Cook's membrane
is pending its transcribed reference. docs/fem.md describes the
formulation, the material point interface, the follower-pressure choice and
what nonlinear steps refuse; the literature, parity and roadmap pages
follow.

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

tests/oracle/nl-rigid-rotation/expected.json

@@ -0,0 +1,83 @@
+{
+ "title": "A quarter turn strains and stresses nothing (objectivity)",
+ "kind": "theory",
+ "source": "Objectivity of the total Lagrangian formulation and of the hyperelastic stress: a rigid motion x = R X + c gives C = I and σ = 0 whatever the rotation (Bonet & Wood 2008, §3.4 and §5.2; T. Belytschko, W. K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, 2nd ed., Wiley 2014, §5.5)",
+ "quantities": [
+  {
+   "id": "ux",
+   "quantity": "u_x at inner node 22: the rotation's",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Turn",
+     "nodes": [
+      22
+     ]
+    },
+    "pointer": "/nodes/0/displacement/0"
+   },
+   "value": -0.011149180525904245,
+   "tolerance": {
+    "absolute": 1e-09
+   },
+   "reason": "the inner nodes follow the rigid rotation exactly"
+  },
+  {
+   "id": "uy",
+   "quantity": "u_y at inner node 22: the rotation's",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Turn",
+     "nodes": [
+      22
+     ]
+    },
+    "pointer": "/nodes/0/displacement/1"
+   },
+   "value": 0.07859051161172886,
+   "tolerance": {
+    "absolute": 1e-09
+   },
+   "reason": "the inner nodes follow the rigid rotation exactly"
+  },
+  {
+   "id": "uz",
+   "quantity": "u_z at inner node 22: the rotation's",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Turn",
+     "nodes": [
+      22
+     ]
+    },
+    "pointer": "/nodes/0/displacement/2"
+   },
+   "value": -0.06744133108582467,
+   "tolerance": {
+    "absolute": 1e-09
+   },
+   "reason": "the inner nodes follow the rigid rotation exactly"
+  },
+  {
+   "id": "von_mises",
+   "quantity": "von Mises stress at inner node 22",
+   "measure": {
+    "command": "solve.probe",
+    "params": {
+     "step": "Turn",
+     "nodes": [
+      22
+     ]
+    },
+    "pointer": "/nodes/0/von_mises"
+   },
+   "value": 0.0,
+   "tolerance": {
+    "absolute": 1e-08
+   },
+   "reason": "zero up to rounding of stresses of order E = 1000: a 90° turn leaves no strain"
+  }
+ ]
+}