{
  "case": "elastoplastic / uniaxial bar, J2 isotropic hardening",
  "material": {
    "E_Pa": 210000000000.0,
    "nu": 0.3,
    "yield_stress_Pa": 250000000.0,
    "hardening_H_Pa": 2000000000.0
  },
  "geometry": {
    "L_m": 500.0,
    "cross_section_m": [
      50.0,
      50.0
    ]
  },
  "eps_yield": 0.0011904761904761906,
  "method": "closed form derived from code's R(alpha)=H*alpha isotropic hardening law (plasticity_j2.py HardeningLaw); stress read from fixed-end reaction force / area (equilibrium-exact, end-effect free average axial stress)",
  "points": [
    {
      "eps_target": 0.0008,
      "sigma_fem_Pa": 170150286.91596523,
      "sigma_closed_form_Pa": 168000000.0,
      "reaction_force_N": -425375717289.9131,
      "max_von_mises_Pa": 177132949.10762438,
      "error_pct": 1.2799326880745412,
      "elapsed_s": 367.5510184764862
    },
    {
      "eps_target": 0.0013,
      "sigma_fem_Pa": 250136448.05935737,
      "sigma_closed_form_Pa": 250216981.13207546,
      "reaction_force_N": -625341120148.3934,
      "max_von_mises_Pa": 250438224.51028234,
      "error_pct": 0.03218529468052969,
      "elapsed_s": 962.3156831264496
    },
    {
      "eps_target": 0.0018,
      "sigma_fem_Pa": 251871072.7733994,
      "sigma_closed_form_Pa": 251207547.1698113,
      "reaction_force_N": -629677681933.4985,
      "max_von_mises_Pa": 251693069.54002786,
      "error_pct": 0.2641344223386625,
      "elapsed_s": 1224.9846959114075
    },
    {
      "eps_target": 0.0028,
      "sigma_fem_Pa": 255255411.45944253,
      "sigma_closed_form_Pa": 253188679.245283,
      "reaction_force_N": -638138528648.6063,
      "max_von_mises_Pa": 254629212.99685812,
      "error_pct": 0.8162814468325098,
      "elapsed_s": 1820.0035588741302
    },
    {
      "eps_target": 0.0042,
      "sigma_fem_Pa": 259793784.96791056,
      "sigma_closed_form_Pa": 255962264.1509434,
      "reaction_force_N": -649484462419.7764,
      "max_von_mises_Pa": 258611016.2435969,
      "error_pct": 1.4969084719096228,
      "elapsed_s": 2706.5675325393677
    }
  ],
  "max_error_pct": 1.4969084719096228,
  "pass": true
}