{
 "title": "A steel bar held at its ends and heated past yield (small strain)",
 "kind": "theory",
 "source": "Uniaxial J2 plasticity with linear hardening (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) with the additive thermal strain: the bar's total axial strain is held at zero, so its mechanical strain is −α ΔT and σ = −(σ_y + E_t (α ΔT − σ_y/E)) once α ΔT exceeds σ_y/E",
 "quantities": [
  {
   "id": "sigma",
   "quantity": "axial stress, ΔT = 300 (α ΔT = 3.6·10⁻³, 2.9 times the yield strain)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Heat",
     "elements": [
      2
     ]
    },
    "pointer": "/elements/0/stress/0/0"
   },
   "value": -254.65346534653466,
   "tolerance": {
    "relative": 1e-08
   },
   "reason": "a homogeneous uniaxial state the elements represent exactly"
  },
  {
   "id": "plastic_strain",
   "quantity": "equivalent plastic strain",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Heat",
     "elements": [
      2
     ]
    },
    "pointer": "/elements/0/plastic_strain/0"
   },
   "value": 0.0023267326732673297,
   "tolerance": {
    "relative": 1e-07
   },
   "reason": "(|σ| − σ_y)/H, as for the stress"
  }
 ]
}