{
 "title": "Free and fully constrained thermal expansion at finite strain",
 "kind": "theory",
 "source": "The multiplicative split F = F_m F_θ with F_θ = (1 + α ΔT) I (V. A. Lubarda, Appl. Mech. Rev. 57(2):95–108, 2004): a free body follows F = F_θ stress-free; held on every face, F = I and F_m = ϑ⁻¹ I, so the compressible neo-Hookean material carries the pressure of its volume ratio, σ = κ (ϑ⁻³ − 1)",
 "quantities": [
  {
   "id": "free_u",
   "quantity": "displacement of the corner (1, 1, 1) along x, free, α ΔT = 0.2",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Free",
     "at": [
      [
       1,
       1,
       1
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 0.2,
   "tolerance": {
    "relative": 1e-08
   },
   "reason": "a homogeneous stretch every element represents exactly"
  },
  {
   "id": "free_stress",
   "quantity": "stress of the free body (σ_xx at the corner)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Free",
     "at": [
      [
       1,
       1,
       1
      ]
     ]
    },
    "pointer": "/nodes/0/stress/0"
   },
   "value": 0.0,
   "tolerance": {
    "absolute": 1e-08
   },
   "reason": "rounding only"
  },
  {
   "id": "held_stress",
   "quantity": "stress of the held block, σ_xx (hydrostatic)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Held",
     "at": [
      [
       0.5,
       0.5,
       0.5
      ]
     ]
    },
    "pointer": "/nodes/0/stress/0"
   },
   "value": -3.5108024691358017,
   "tolerance": {
    "relative": 1e-08
   },
   "reason": "a homogeneous state; E = 10, ν = 0.3 (κ = 8.3333), ϑ = 1.2"
  }
 ]
}