{
  "case": "thermal_stress / axially-restrained bar, uniform temperature rise",
  "citation": "Standard restrained thermal expansion result, sigma = -E*alpha*delta_T (e.g. Boresi & Schmidt, Advanced Mechanics of Materials)",
  "geometry": {
    "L_m": 1.0,
    "cross_section_m": [
      0.05,
      0.05
    ]
  },
  "material": {
    "E_Pa": 210000000000.0,
    "nu": 0.3,
    "alpha_1_K": 1.2e-05,
    "k_W_mK": 50.0,
    "T_ref_K": 293.15
  },
  "delta_T_K": 100.0,
  "method": "Temperature forced uniform (fixed_temp on all 6 faces at the same value); axial displacement restrained at both ends, lateral faces free; stress read directly from the interior (mid-bar) stress field, well away from either end.",
  "sigma_exact_Pa": -252000000.0,
  "sigma_fem_Pa": -255017246.64147508,
  "error_pct": 1.197320095823445,
  "temp_uniformity_max_deviation_K": 1.0440642142839351e-05,
  "pass": true,
  "elapsed_s": 54.21628522872925
}