{
 "title": "Uniaxial tension of a J2 bilinear-hardening cube to large strain (explicit)",
 "kind": "theory",
 "source": "von Mises plasticity with linear isotropic hardening under uniaxial stress (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3); logarithmic strain for a hypoelastic–plastic law under coaxial stretching",
 "quantities": [
  {
   "id": "sigma",
   "quantity": "axial Cauchy stress at a logarithmic strain of 0.2",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      1
     ]
    },
    "pointer": "/elements/0/stress/0"
   },
   "value": 643.5643564356436,
   "tolerance": {
    "relative": 0.01
   },
   "reason": "uniaxial J2 with linear hardening: σ = σ_y + E_t (ε − σ_y/E) in logarithmic strain; the stretch takes 10⁴ wave transits, so inertia and the ringing of the start (ρcv ≈ 0.1% of σ) stay well under 1%"
  },
  {
   "id": "plastic_strain",
   "quantity": "equivalent plastic strain",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      1
     ]
    },
    "pointer": "/elements/0/plastic_strain"
   },
   "value": 0.1967821782178218,
   "tolerance": {
    "relative": 0.01
   },
   "reason": "ε_p = ε − σ/E, as for the stress"
  }
 ]
}