{
  "case": "hyperelastic / Treloar (1944) pure shear (planar tension) -- 3-term Ogden, combined UT+ET+PS fit (see treloar_fit.py)",
  "citation": "Treloar, L.R.G. (1944), Trans. Faraday Soc. 40; data digitized via github.com/OVGU-CoMe/treloar_fit (Data_Treloar_PS.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_PS": 0.8291590150646252,
    "fit_rms_pct_of_range_PS": 9.707748119032544,
    "fit_note": "SAME combined UT+ET+PS fit as case_01/case_02 -- see treloar_fit.py."
  },
  "geometry": {
    "L_m": 4.0,
    "W_m": 8.0,
    "thickness_m": 0.5
  },
  "method": "Real Treloar-measured STRETCH applied as an axial-only displacement BC; width rigidly gripped (uy=0) on both long edges to enforce the plane-strain pure-shear state; FEM nominal stress (from Cauchy stress at the known homogeneous J) compared directly to Treloar's actual measured stress.",
  "points": [
    {
      "lambda1_data": 1.14,
      "S_data_MPa": 0.1404,
      "lambda1_fem": 1.14,
      "lambda3_fem_thickness": 0.8816508959416592,
      "P1_fem_MPa": 0.10424735929426422,
      "P1_closedform_MPa": 0.10424735929408681,
      "fem_vs_data_error_pct": 25.7497440924044,
      "fem_vs_closedform_error_pct": 1.7018843610584602e-10,
      "elapsed_s": 12.909944772720337
    },
    {
      "lambda1_data": 1.32,
      "S_data_MPa": 0.25,
      "lambda1_fem": 1.32,
      "lambda3_fem_thickness": 0.7656403781239753,
      "P1_fem_MPa": 0.1911018388051002,
      "P1_closedform_MPa": 0.19110183880509884,
      "fem_vs_data_error_pct": 23.559264477959914,
      "fem_vs_closedform_error_pct": 7.157859076707049e-13,
      "elapsed_s": 12.458890438079834
    },
    {
      "lambda1_data": 1.87,
      "S_data_MPa": 0.3155,
      "lambda1_fem": 1.87,
      "lambda3_fem_thickness": 0.5472998892212195,
      "P1_fem_MPa": 0.3066416611712108,
      "P1_closedform_MPa": 0.30664166117127684,
      "fem_vs_data_error_pct": 2.807714367286607,
      "fem_vs_closedform_error_pct": 2.154491822292994e-11,
      "elapsed_s": 14.646121263504028
    },
    {
      "lambda1_data": 2.98,
      "S_data_MPa": 0.3121,
      "lambda1_fem": 2.9800000000000004,
      "lambda3_fem_thickness": 0.3491126105578568,
      "P1_fem_MPa": 0.3466192773229104,
      "P1_closedform_MPa": 0.3466192773228938,
      "fem_vs_data_error_pct": 11.060325960560856,
      "fem_vs_closedform_error_pct": 4.785995599686317e-12,
      "elapsed_s": 12.104882717132568
    },
    {
      "lambda1_data": 3.96,
      "S_data_MPa": 0.3232,
      "lambda1_fem": 3.9600000000000004,
      "lambda3_fem_thickness": 0.2657389456337318,
      "P1_fem_MPa": 0.35248196926980085,
      "P1_closedform_MPa": 0.3524819692697709,
      "fem_vs_data_error_pct": 9.060015244369083,
      "fem_vs_closedform_error_pct": 8.504532992861532e-12,
      "elapsed_s": 12.59425950050354
    },
    {
      "lambda1_data": 4.69,
      "S_data_MPa": 0.3454,
      "lambda1_fem": 4.690000000000001,
      "lambda3_fem_thickness": 0.2265409146219719,
      "P1_fem_MPa": 0.3703078650563269,
      "P1_closedform_MPa": 0.37030786505630875,
      "fem_vs_data_error_pct": 7.211310091582774,
      "fem_vs_closedform_error_pct": 4.904241016387895e-12,
      "elapsed_s": 12.996384859085083
    }
  ],
  "max_fem_vs_closedform_error_pct": 1.7018843610584602e-10,
  "rms_fem_vs_data_MPa": 0.03541161052965023,
  "r2_fem_vs_data": 0.7388893490804147,
  "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-PS-data R^2 must be >= 0.7. Achieved R^2=0.7389. Same threshold as case_01/case_02, not tuned per case.",
  "pass": true
}