{
  "case": "hyperelastic / Treloar (1944) uniaxial tension -- 3-term Ogden fit to REAL experimental data",
  "citation": "Treloar, L.R.G. (1944), Trans. Faraday Soc. 40; data digitized via github.com/OVGU-CoMe/treloar_fit (Data_Treloar_UT.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_UT": 0.9766181410956023,
    "fit_rms_pct_of_range_UT": 3.7478793168406126,
    "fit_note": "combined nonlinear least squares against UT+ET+PS simultaneously (see treloar_fit.py); NOT fit to UT alone."
  },
  "geometry": {
    "L_m": 4.0,
    "cross_section_m": [
      2.0,
      2.0
    ]
  },
  "method": "Real Treloar-measured STRETCH applied as an axial-only displacement BC (lateral faces free); FEM nominal stress (from Cauchy stress at the known homogeneous J) compared directly to Treloar's actual measured stress.",
  "points": [
    {
      "lambda1_data": 1.12,
      "S_data_MPa": 0.125,
      "lambda1_fem": 1.12,
      "P1_fem_MPa": 0.07031806944686349,
      "P1_closedform_MPa": 0.07031806944756508,
      "fem_vs_data_error_pct": 43.74554444250921,
      "fem_vs_closedform_error_pct": 9.97739975538457e-10,
      "elapsed_s": 13.057673215866089
    },
    {
      "lambda1_data": 1.39,
      "S_data_MPa": 0.2302,
      "lambda1_fem": 1.39,
      "P1_fem_MPa": 0.16768044820995154,
      "P1_closedform_MPa": 0.1676804482105261,
      "fem_vs_data_error_pct": 27.158797476128782,
      "fem_vs_closedform_error_pct": 3.426564199992211e-10,
      "elapsed_s": 11.731049060821533
    },
    {
      "lambda1_data": 1.89,
      "S_data_MPa": 0.2646,
      "lambda1_fem": 1.8899999999999997,
      "P1_fem_MPa": 0.24542490975443834,
      "P1_closedform_MPa": 0.24542490975862885,
      "fem_vs_data_error_pct": 7.2468217103407575,
      "fem_vs_closedform_error_pct": 1.7074411593361148e-09,
      "elapsed_s": 12.727575778961182
    },
    {
      "lambda1_data": 2.42,
      "S_data_MPa": 0.2769,
      "lambda1_fem": 2.42,
      "P1_fem_MPa": 0.27393576594358865,
      "P1_closedform_MPa": 0.2739357659593434,
      "fem_vs_data_error_pct": 1.0705070626259912,
      "fem_vs_closedform_error_pct": 5.7512667197615685e-09,
      "elapsed_s": 12.542811632156372
    },
    {
      "lambda1_data": 3.58,
      "S_data_MPa": 0.2905,
      "lambda1_fem": 3.58,
      "P1_fem_MPa": 0.2916181540284376,
      "P1_closedform_MPa": 0.29161815414079373,
      "fem_vs_data_error_pct": 0.3849067223537433,
      "fem_vs_closedform_error_pct": 3.852849782581321e-08,
      "elapsed_s": 11.801709651947021
    },
    {
      "lambda1_data": 5.36,
      "S_data_MPa": 0.3619,
      "lambda1_fem": 5.36,
      "P1_fem_MPa": 0.36475670180259234,
      "P1_closedform_MPa": 0.36475670256402204,
      "fem_vs_data_error_pct": 0.7893622002189327,
      "fem_vs_closedform_error_pct": 2.087500286277101e-07,
      "elapsed_s": 15.467002391815186
    },
    {
      "lambda1_data": 6.4,
      "S_data_MPa": 0.4719,
      "lambda1_fem": 6.3999999999999995,
      "P1_fem_MPa": 0.49100713297042003,
      "P1_closedform_MPa": 0.49100713461039075,
      "fem_vs_data_error_pct": 4.04897922662006,
      "fem_vs_closedform_error_pct": 3.340013981609231e-07,
      "elapsed_s": 12.385181665420532
    },
    {
      "lambda1_data": 6.87,
      "S_data_MPa": 0.5459,
      "lambda1_fem": 6.869999999999999,
      "P1_fem_MPa": 0.5769858451804918,
      "P1_closedform_MPa": 0.5769858473567092,
      "fem_vs_data_error_pct": 5.694421172465983,
      "fem_vs_closedform_error_pct": 3.7716997661856423e-07,
      "elapsed_s": 14.014675617218018
    },
    {
      "lambda1_data": 7.16,
      "S_data_MPa": 0.6243,
      "lambda1_fem": 7.16,
      "P1_fem_MPa": 0.6398641527571817,
      "P1_closedform_MPa": 0.6398641553039,
      "fem_vs_data_error_pct": 2.4930566646134342,
      "fem_vs_closedform_error_pct": 3.9800920344842535e-07,
      "elapsed_s": 12.860326290130615
    },
    {
      "lambda1_data": 7.43,
      "S_data_MPa": 0.7012,
      "lambda1_fem": 7.43,
      "P1_fem_MPa": 0.7052916251218385,
      "P1_closedform_MPa": 0.7052916280384867,
      "fem_vs_data_error_pct": 0.5835175587333898,
      "fem_vs_closedform_error_pct": 4.135378973885925e-07,
      "elapsed_s": 13.5655996799469
    },
    {
      "lambda1_data": 7.61,
      "S_data_MPa": 0.8279,
      "lambda1_fem": 7.61,
      "P1_fem_MPa": 0.7526150958093714,
      "P1_closedform_MPa": 0.7526150989849766,
      "fem_vs_data_error_pct": 9.093477979300479,
      "fem_vs_closedform_error_pct": 4.2194279774223323e-07,
      "elapsed_s": 13.207019329071045
    }
  ],
  "max_fem_vs_closedform_error_pct": 4.2194279774223323e-07,
  "rms_fem_vs_data_MPa": 0.036360446810994734,
  "r2_fem_vs_data": 0.9704800066071955,
  "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-data R^2 must be >= 0.7 for this loading mode. Achieved R^2=0.9705. Threshold is set below the R^2=0.9766 the underlying combined fit achieves on UT (see treloar_fit.py) -- not tuned to this run.",
  "pass": true
}