{
 "title": "Nearly incompressible hybrid block under prescribed stretch",
 "kind": "theory",
 "source": "Uniaxial stress of the decoupled compressible neo-Hookean energy W = μ/2 (Ī₁ − 3) + κ/2 (J − 1)² (P. J. Flory, Trans. Faraday Soc. 57:829–838, 1961): σ = μ J^(−5/3) (λ² − I₁/3) + κ (J − 1) with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.4999: μ = 1.0000667, κ = 5000)",
 "quantities": [
  {
   "id": "sigma",
   "quantity": "axial Cauchy stress, stretch λ = 2, ν = 0.4999",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Uniaxial",
     "at": [
      [
       1,
       1,
       1
      ]
     ]
    },
    "pointer": "/nodes/0/stress/0"
   },
   "value": 3.498756466061613,
   "tolerance": {
    "relative": 1e-06
   },
   "reason": "a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): the tolerance admits the Newton tolerance and rounding"
  },
  {
   "id": "lateral",
   "quantity": "lateral displacement at (1, 1, 1): l − 1",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Uniaxial",
     "at": [
      [
       1,
       1,
       1
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/1"
   },
   "value": -0.29281075714096483,
   "tolerance": {
    "relative": 1e-06
   },
   "reason": "a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): the tolerance admits the Newton tolerance and rounding"
  }
 ]
}