{
  "case": "hyperelastic / Treloar (1944) equibiaxial tension -- 3-term Ogden, combined UT+ET+PS fit (see module docstring: NOT a blind cross-mode prediction)",
  "citation": "Treloar, L.R.G. (1944), Trans. Faraday Soc. 40; data digitized via github.com/OVGU-CoMe/treloar_fit (Data_Treloar_ET.mat)",
  "fitted_material": {
    "nu_fixed": 0.49,
    "ogden_mu_Pa": [
      230881.76869550248,
      100.00000000000001,
      100.00000000000001
    ],
    "ogden_alpha": [
      0.3192002476687631,
      5.891675109537164,
      -3.029004560337629
    ],
    "fit_r2_ET": 0.8524661638072197,
    "fit_rms_pct_of_range_ET": 8.967463397393802,
    "fit_note": "SAME combined UT+ET+PS fit as case_01/case_03 -- see treloar_fit.py."
  },
  "geometry": {
    "side_m": 4.0,
    "thickness_m": 0.5
  },
  "method": "Real Treloar-measured STRETCH applied as axial-only displacement BCs on both in-plane faces (thickness free); FEM nominal stress (from Cauchy stress at the known homogeneous J) compared directly to Treloar's actual measured stress.",
  "points": [
    {
      "lambda_data": 1.08,
      "S_data_MPa": 0.1481,
      "lambda_fem": 1.08,
      "lambda3_fem_thickness": 0.8624259918656836,
      "P_fem_MPa": 0.09514619901638333,
      "P_closedform_MPa": 0.09514619901633069,
      "fem_vs_data_error_pct": 35.75543618069999,
      "fem_vs_closedform_error_pct": 5.531936948103294e-11,
      "elapsed_s": 18.327289819717407
    },
    {
      "lambda_data": 1.14,
      "S_data_MPa": 0.2281,
      "lambda_fem": 1.14,
      "lambda3_fem_thickness": 0.7771511452426771,
      "P_fem_MPa": 0.15230273311555884,
      "P_closedform_MPa": 0.15230273311543363,
      "fem_vs_data_error_pct": 33.229840808610774,
      "fem_vs_closedform_error_pct": 8.220776874041583e-11,
      "elapsed_s": 11.62590742111206
    },
    {
      "lambda_data": 1.31,
      "S_data_MPa": 0.3359,
      "lambda_fem": 1.31,
      "lambda3_fem_thickness": 0.5943735867671966,
      "P_fem_MPa": 0.26815180208495437,
      "P_closedform_MPa": 0.2681518020845981,
      "fem_vs_data_error_pct": 20.16915686664055,
      "fem_vs_closedform_error_pct": 1.3286843112056724e-10,
      "elapsed_s": 12.727406978607178
    },
    {
      "lambda_data": 1.69,
      "S_data_MPa": 0.3846,
      "lambda_fem": 1.69,
      "lambda3_fem_thickness": 0.3631296110178812,
      "P_fem_MPa": 0.39232654643616005,
      "P_closedform_MPa": 0.3923265464348851,
      "fem_vs_data_error_pct": 2.00898243269892,
      "fem_vs_closedform_error_pct": 3.2496460119077793e-10,
      "elapsed_s": 13.495785236358643
    },
    {
      "lambda_data": 2.49,
      "S_data_MPa": 0.3855,
      "lambda_fem": 2.49,
      "lambda3_fem_thickness": 0.17122639661537176,
      "P_fem_MPa": 0.4522923300389817,
      "P_closedform_MPa": 0.45229233003270375,
      "fem_vs_data_error_pct": 17.32615565213534,
      "fem_vs_closedform_error_pct": 1.388037525944357e-09,
      "elapsed_s": 11.68930959701538
    },
    {
      "lambda_data": 3.43,
      "S_data_MPa": 0.4227,
      "lambda_fem": 3.43,
      "lambda3_fem_thickness": 0.09225121833850092,
      "P_fem_MPa": 0.46480564987161327,
      "P_closedform_MPa": 0.46480564985622674,
      "fem_vs_data_error_pct": 9.961118966551513,
      "fem_vs_closedform_error_pct": 3.3103075823849142e-09,
      "elapsed_s": 13.278563976287842
    },
    {
      "lambda_data": 4.03,
      "S_data_MPa": 0.4864,
      "lambda_fem": 4.030000000000001,
      "lambda3_fem_thickness": 0.06798837586616346,
      "P_fem_MPa": 0.49147085330089724,
      "P_closedform_MPa": 0.4914708533064019,
      "fem_vs_data_error_pct": 1.042527405612095,
      "fem_vs_closedform_error_pct": 1.1200339242689321e-09,
      "elapsed_s": 14.0479154586792
    },
    {
      "lambda_data": 4.44,
      "S_data_MPa": 0.5473,
      "lambda_fem": 4.440000000000001,
      "lambda3_fem_thickness": 0.05688052161136703,
      "P_fem_MPa": 0.5274731575928772,
      "P_closedform_MPa": 0.5274731576694927,
      "fem_vs_data_error_pct": 3.622664426662313,
      "fem_vs_closedform_error_pct": 1.4525001569727684e-08,
      "elapsed_s": 14.038545370101929
    }
  ],
  "max_fem_vs_closedform_error_pct": 1.4525001569727684e-08,
  "rms_fem_vs_data_MPa": 0.04981436399588132,
  "r2_fem_vs_data": 0.8327507986490563,
  "solver_pass": true,
  "solver_pass_criterion": "SECONDARY sanity check: FEM must reproduce the code's own closed-form root-solve to <1%% -- proves solver/BC-implementation correctness, says nothing about real-rubber accuracy on its own.",
  "data_pass": true,
  "data_pass_criterion": "PRIMARY pass gate: FEM-vs-REAL-Treloar-ET-data R^2 must be >= 0.7. Achieved R^2=0.8328. Same threshold as case_01/case_03, not tuned per case.",
  "pass": true
}