{
 "title": "Inflation of a thick neo-Hookean cylinder by a follower pressure (plane strain)",
 "kind": "theory",
 "source": "Finite inflation of an incompressible neo-Hookean thick-walled tube in plane strain: r² = R² + a² − A², σ_θ − σ_r = μ (λ² − λ⁻²) with λ = r/R, integrated through the wall: p = (μ/2)[(ln λ_a² − λ_a⁻²) − (ln λ_b² − λ_b⁻²)] (R. S. Rivlin, Large elastic deformations of isotropic materials VI, Phil. Trans. R. Soc. A 242:173–195, 1949; R. W. Ogden, Non-Linear Elastic Deformations, Dover 1997, §5.3.2)",
 "quantities": [
  {
   "id": "ua",
   "quantity": "radial displacement of the bore (10, 0, 0) at the pressure that inflates it to a = 15",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Inflate",
     "at": [
      [
       10.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 5.0,
   "tolerance": {
    "relative": 0.005
   },
   "reason": "the closed form is incompressible and our material nearly so (κ/μ = 1000, a volume change of order p/κ ≈ 4·10⁻⁴); hybrid hex20, 6 × 16, follow the wall's strain gradient well inside"
  },
  {
   "id": "ub",
   "quantity": "radial displacement of the outer wall (20, 0, 0)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Inflate",
     "at": [
      [
       20.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 2.9128784747791983,
   "tolerance": {
    "relative": 0.005
   },
   "reason": "as at the bore"
  }
 ]
}