Skip to content

elhajjar1/wrinkleFE

Repository files navigation

WrinkleFE

Open in Streamlit License: MIT DOI Python GitHub stars

An open-source Python finite element package for predicting strength and stiffness knockdown in composite laminates containing fiber waviness defects.

Found WrinkleFE useful? Please star the repository and cite it — it's a free academic project, and stars and citations are what keep it supported.

Try it in your browser

The fastest way to use WrinkleFE is the hosted Streamlit app — no install required:

Pick a material, set the wrinkle amplitude / wavelength / morphology, and the app returns the analytical knockdown, plots, and (optionally) a full FE solve. Public link, no account needed.

Features

  • Compression model: CLT-weighted Budiansky-Fleck kink-band with layup-dependent confinement
  • Tension model: Three-mechanism (fiber cos^2 theta, Hashin matrix, curved-beam sigma_33 delamination) with thick-ply in-situ correction
  • 3D finite element: Structured hexahedral mesh with LaRC04/05 failure criteria
  • Five morphologies: Stack, convex, concave, uniform, graded (with configurable decay floor)
  • Graded averaging: Through-thickness ply-averaged knockdown for graded wrinkles
  • Movable wrinkle position: Configurable through-thickness placement (wrinkle_z_position, 0.5 = mid-plane)
  • Resin-pocket material zone: Graded neat-epoxy lens at the wrinkle crest (modulus + fibre-angle blend, counted once) via wrinklefe.core.resin_pocket
  • Progressive-damage FE: Load-stepping ProgressiveDamageSolver to ultimate load with optional crack-band (Bažant–Oh) regularization — the first FE route to a UD compression knockdown
  • Penetration gate (θ, D/T, z): Closed-form two-parameter UD predictor KD = 1 − (1 − KD_angle(θ))·S(D/T)·P(z) with calibrated presets; zero FE cost (wrinklefe.core.penetration_gate)
  • Linear buckling: Geometric-stiffness eigenvalue solve (LinearBucklingSolver) with a microbuckling knockdown — verified structural-buckling infrastructure, but a homogenised-continuum eigenvalue does not capture the fibre-scale wrinkle knockdown (it gets the sign wrong: the bifurcation load rises with the wrinkle), so it is not the production UD predictor (the penetration gate is); see the modelling findings
  • 11 built-in laminate materials (AS4/3501-6, IM7/8552, T300/914, T700/2510, AC318/S6C10 S-glass/epoxy, T800S/M21, IM10/8552, IM6G/3501-6 carbon/epoxy — the Hsiao & Daniel 1996 wavy-UD study, S-2 glass/epoxy, Kevlar-49/epoxy, plus AC318_S6C10_vacbag — the Li 2025 vacuum-bag realization, measured Xc=335.5 MPa, E1=50.8 GPa) plus an isotropic neat-epoxy card (EPOXY_S6C10) for the resin-pocket zone
  • Comprehensive test suite covering all modules (run pytest to see the current count)

Developer / library install

If you want to script against the package or contribute to development:

pip install wrinklefe

Or install the latest source:

git clone https://github.com/elhajjar1/wrinklefe.git
cd wrinklefe
pip install -e ".[all]"

Verify the install:

python -c "import wrinklefe; print('WrinkleFE installed successfully')"

Run the test suite:

pytest

Quick Start

Streamlit web app

The fastest path is the hosted Streamlit instance — no install, no Python required: https://wrinklefe.streamlit.app/. Pick a material from the sidebar (or Custom… to enter your own elastic constants and strength allowables), enter a layup in contracted notation (e.g. [0/45/-45/90]_3s), set the wrinkle geometry, and click Run analysis. The app ships with per-morphology schematic cartoons, a live wrinkle preview, and the same analytical + FE pipeline as the Python API. See DEPLOYMENT_STREAMLIT.md for the full feature tour and instructions for self-hosting.

To run the app locally:

pip install -r requirements.txt
pip install -e .
streamlit run app.py

Python API

from wrinklefe.analysis import AnalysisConfig, WrinkleAnalysis

config = AnalysisConfig(
    amplitude=0.366, wavelength=16.0, width=12.0,
    morphology="stack", loading="compression",
)
result = WrinkleAnalysis(config).run()
print(result.summary())

Runnable scripts for the common workflows — parametric sweeps, morphology comparison, CZM delamination, export round-trips, custom materials — live in examples/; each states its expected runtime and output, and CI executes them all so they stay current. The full API reference and user guide are built from docs/ with Sphinx (pip install -e ".[docs]" && sphinx-build -W docs docs/_build) and published at https://wrinklefe.readthedocs.io.

amplitude (A) is the half-amplitude [mm]: the peak displacement of the wrinkled mid-surface from the flat (unwrinkled) reference plane, so z(x) = A·cos(2πx/λ) (modulated by the envelope) and the peak-to-trough height is 2A. For a measured wrinkle (e.g. from a cross-section micrograph or CT slice), A = (z_max − z_min) / 2. The peak fibre misalignment angle scales as θ_max ≈ arctan(2πA/λ), which drives the Budiansky-Fleck compressive knockdown.

Wrinkle geometry parameters

All wrinkle length parameters use a single, consistent unit: millimetres (mm) — the same unit as ply_thickness and domain_length (the default amplitude=0.366 mm is exactly two ply thicknesses of 0.183 mm). Lengths are not normalized by thickness. The longitudinal coordinate x runs along the laminate in the fibre direction; out-of-plane displacement z(x) is measured from the flat (undeformed) mid-surface. Angles are in radians.

This table is the canonical reference for every wrinkle-geometry parameter exposed by AnalysisConfig, the CLI, and the Streamlit UI. The AnalysisConfig docstrings, CLI --help, and Streamlit help= tooltips all mirror these definitions; the tests/test_param_docs_match.py regression test pins the defaults so the docs and the dataclass cannot drift.

Parameter Units Default Definition Constraint
amplitude (A) mm 0.366 Half-amplitude: peak displacement of the wrinkled mid-surface from the flat reference, with z(x) = A·cos(2π(x − x₀)/λ) (modulated by the envelope) and peak-to-trough height 2A. For a measured wrinkle, A = (z_max − z_min)/2. ≥ 0 (0 = flat / no wrinkle)
wavelength (λ) mm 16.0 Spatial period of the cos(2π(x − x₀)/λ) carrier along the longitudinal x-direction (crest-to-crest distance). Wavenumber k = 2π/λ. > 0
width (w) mm 12.0 Longitudinal envelope decay length about the centre x₀. Exact meaning is profile-dependent: Gaussian 1/e length scale in exp(−(x−x₀)²/w²), tapered flat-top extent (|x−x₀| < w/2), or triangular half-base (|x−x₀| < w). Also used as the transverse (y-direction) extent of the wrinkle in 3-D dual-wrinkle / graded mesh deformation. > 0
phase (φ) rad None Explicit dual-wrinkle phase offset between the two wrinkle centrelines. None derives φ from morphology via MORPHOLOGY_PHASES (stack φ=0, convex φ=+π/2, concave φ=−π/2). A float overrides the named-morphology phase so arbitrary offsets can be swept (e.g. 0 to π). Ignored for single-wrinkle morphologies (uniform, graded). finite when set
decay_floor dimensionless 0.0 Graded morphology only: minimum fraction of the wrinkle amplitude retained at the laminate outer surfaces. 0.0 = full decay to zero amplitude at the surfaces (pure graded); 1.0 = no decay (equivalent to uniform). in [0, 1]
amplitude_profile name "constant" Spatially varying in-plane modulation of the wrinkle amplitude A, applied on top of the wrinkle's own longitudinal envelope. "constant" (default) preserves the legacy uniform A; "gaussian" multiplies A by exp(−(s/d)²); "linear" multiplies A by max(0, 1 − |s|/d) (clipped). s is the coordinate from the wrinkle centre along amplitude_profile_axis and d is amplitude_profile_decay_length. one of constant, gaussian, linear
amplitude_profile_decay_length mm None Decay length d (mm) for the Gaussian sigma or linear-decay extent. None falls back to the wrinkle profile's own width. Ignored when amplitude_profile == "constant". finite and > 0 when set
amplitude_profile_axis axis "x" In-plane axis along which the amplitude modulation runs. Pick "y" for an independent transverse tapering of A that does not stack with the existing longitudinal envelope on x. one of x, y

Peak fibre misalignment: θ_max ≈ arctan(2πA/λ) (exact for a pure cosine; dimensionless because A and λ share the mm length unit). See the WrinkleProfile class docstring in src/wrinklefe/core/wrinkle.py for the full per-profile geometric definitions.

Tension analysis

config = AnalysisConfig(
    amplitude=0.366, wavelength=16.0, width=12.0,
    morphology="stack", loading="tension",
    angles=[0, 45, 90, -45, 0, 45, -45, 0, 0, -45, 45, 0, -45, 90, 45, 0],
    ply_thickness=0.152,
)
result = WrinkleAnalysis(config).run()
print(result.summary())

Graded morphology (embedded wrinkle)

config = AnalysisConfig(
    amplitude=0.5, wavelength=15.0, width=11.0,
    morphology="graded", decay_floor=0.0,
    loading="compression",
)
result = WrinkleAnalysis(config).run()
print(result.analytical_knockdown)

Resin pocket + progressive-damage FE (UD compression)

For a unidirectional wrinkle, tag the soft neat-epoxy lens at the crest and load-step to ultimate with the progressive-damage solver:

from wrinklefe.analysis import AnalysisConfig, WrinkleAnalysis
from wrinklefe.core.material import MaterialLibrary

lib = MaterialLibrary()
config = AnalysisConfig(
    amplitude=0.366, wavelength=16.0, width=12.0,
    morphology="graded", loading="compression",
    material=lib.get("AC318_S6C10"),
    enable_resin_pocket=True,                       # graded epoxy lens at the crest
    resin_pocket_material=lib.get("EPOXY_S6C10"),   # default if left None
    enable_progressive_damage=True,                 # load-step to ultimate
    progressive_n_increments=15,
)
result = WrinkleAnalysis(config).run()
print(result.progressive_knockdown, result.progressive_strength_MPa)

Penetration gate (θ, D/T, z) — UD, zero FE cost

The closed-form two-parameter gate predicts a UD knockdown directly from geometry. Call it on its own with a calibrated preset:

from wrinklefe.core.penetration_gate import penetration_gate_kd, GATE_LI2024_MOULDED

kd = penetration_gate_kd(theta_deg=8.0, dt=0.10, params=GATE_LI2024_MOULDED)
print(kd)

Or drive it through AnalysisConfig.penetration_gate so analytical_knockdown (and analytical_strength_MPa) come from the gate instead of Budiansky–Fleck (use GATE_LI2025_VACBAG with AC318_S6C10_vacbag for the vacuum-bag realization):

from wrinklefe.analysis import AnalysisConfig, WrinkleAnalysis
from wrinklefe.core.material import MaterialLibrary
from wrinklefe.core.penetration_gate import GATE_LI2024_MOULDED

lib = MaterialLibrary()
config = AnalysisConfig(
    amplitude=0.366, wavelength=16.0, width=12.0,
    morphology="uniform", loading="compression",
    material=lib.get("AC318_S6C10"),
    penetration_gate=GATE_LI2024_MOULDED,
)
result = WrinkleAnalysis(config).run(analytical_only=True)
print(result.analytical_knockdown)

When penetration_gate is left unset (the default None), the analytical knockdown is unchanged.

Batch parametric sweeps

For exploring how the knockdown varies across a parameter range, use WrinkleAnalysis.parametric_sweep to sweep a single AnalysisConfig field (any numeric field — amplitude, wavelength, width, phase, applied_strain, ...):

from wrinklefe.analysis import AnalysisConfig, WrinkleAnalysis

base = AnalysisConfig(
    amplitude=0.366, wavelength=16.0, width=12.0,
    morphology="stack", loading="compression",
)
results = WrinkleAnalysis.parametric_sweep(
    base, parameter="amplitude", values=[0.1, 0.2, 0.3, 0.4],
    analytical_only=True,
)
for r in results:
    print(f"A={r.config.amplitude:.3f}  KD={r.analytical_knockdown:.4f}")

For multi-parameter cross-product sweeps with JSON output and plots, use wrinklefe.sweep.run_sweep:

import numpy as np
from wrinklefe.sweep import run_sweep, save_sweep_results, plot_sweep_results

sweep = run_sweep({
    "amplitude":  np.linspace(0.183, 0.549, 3),
    "wavelength": np.linspace(8.0, 24.0, 3),
})
save_sweep_results(sweep, "./sweep_output/")
plot_sweep_results(sweep, "./sweep_output/")

Command line

wrinklefe --help

# Single-parameter sweep (analytical-only is the default, fast)
wrinklefe sweep --parameter amplitude --min 0.1 --max 0.5 --steps 5

Exporting results to CSV / JSON

Numeric outputs (load factor, per-ply failure index, knockdown factors, stress-field summary) can be written to a schema-versioned JSON or a Pandas-friendly per-ply CSV for downstream comparison and plotting in Excel, Pandas, or shared Jupyter notebooks:

from wrinklefe.analysis import AnalysisConfig, WrinkleAnalysis
from wrinklefe.io.results import export_results_csv, export_results_json

result = WrinkleAnalysis(AnalysisConfig()).run()

export_results_json(result, "results.json")  # schema-versioned JSON
export_results_csv(result, "per_ply.csv")    # per-ply tabular CSV

The JSON output is deterministic (sort_keys=True), pins a top-level schema_version field, and reduces large numpy arrays (e.g. per-Gauss-point stress fields) to summary statistics so the file stays compact. The CSV is one row per ply with columns ply_index, angle_deg, max_FI, min_RF, critical_mode, critical_criterion, suitable for pandas.read_csv or csv.DictReader.

Every JSON export carries a provenance block recording the installed WrinkleFE version (never a hardcoded literal), the Python/numpy/scipy versions, the platform, a UTC timestamp, and a solver snapshot — so a result file can be audited and reproduced against the validation ledger. The NCR validation summary (build_analysis_summary) embeds the same block, and the top-level wrinklefe_version field reflects the real installed version.

The Streamlit web app exposes the same exports as Download results as JSON and Download per-ply results as CSV buttons on the Export tab.

Validation

What the in-repo tests check

The integration tests under tests/test_integration/ exercise the full WrinkleAnalysis pipeline and assert physical-sanity properties of the analytical knockdown rather than reproducing absolute experimental strengths:

  • test_elhajjar_validation.py (10 tests): zero-amplitude returns knockdown ≈ 1, knockdown decreases monotonically with amplitude, morphology ordering convex > stack > concave in compression, knockdown stays in (0, 1], and strength equals Xc * knockdown.
  • test_tension_validation.py (13 tests): tension pipeline completes, uses Xt (not Xc), three-mechanism (kd_fiber, kd_matrix, kd_oop) decomposition is populated with the controlling mode, and tension knockdown is no more severe than compression for the same defect.

These act as regression guards on the analytical model. They are not a quantitative validation against experimental data: this repository does not currently ship the Elhajjar (2025), Mukhopadhyay (2015), or Li et al. (2026) experimental data points, nor a script that regenerates case-by-case error statistics. (Tracking issue: #22.)

Quantitative validation against experiment

Comparison of the analytical predictions against published experimental data is documented in the accompanying paper:

Additional datasets referenced by the model calibration (Mukhopadhyay et al., 2015; Li et al., 2026) are cited in References below. Reproducing case-level pass/fail tables from this repository alone is not currently possible — the raw data and regeneration script are not included.

For a consolidated predicted-vs-experimental view, the script validation/plot_all_validation.py regenerates validation/fig_all_validation_parity.png: a single parity plot of every single-wrinkle case (Datasets A–F) inside a ±20% band, with each dataset predicted by the model that physically applies to it (Budiansky–Fleck / three-mechanism for the multidirectional cases A–D, the penetration gate for the UD cases E/F).

Stiffness (modulus) knockdown

Besides strength, WrinkleFE reports a stiffness knockdown of the axial Young's modulus two ways: the FE modulus_retention (wrinkled vs pristine from the linear static solve, any layup) and — for unidirectional layups — a closed-form analytical_modulus_knockdown (a CLT series-average of the off-axis lamina modulus over the wrinkle profile, no FE solve). The script validation/validate_modulus.py scores both against the UD datasets that report a measured modulusF (Li 2025, S-glass), G (Hsiao & Daniel 1996, carbon — the IM6G_3501_6 card), and the indicative E (Li 2024). The analytical estimate lands at 3.9 % MAE (F) / 1.2 % (G) and the FE at 6.9 % (F) / 5.1 % (G). The data and both models agree that stiffness is far more wrinkle-tolerant than strength: the modulus knockdown stays ≈0.81–0.98 for the S-glass cases and only reaches ≈0.52–0.57 for a carbon uniform wrinkle at θ = 15°. The script validation/plot_modulus_validation.py renders the comparison as validation/fig_modulus_validation.png — knockdown-vs-angle and a predicted-vs-experimental parity plot across all three datasets.

Supported morphologies

WrinkleFE ships five wrinkle morphologies (defined in src/wrinklefe/core/morphology.py). They differ along two independent axes: how many wrinkles are placed in the laminate and how the amplitude varies through the thickness. The first three names below are dual-wrinkle modes distinguished by the phase offset φ between two adjacent wrinkle centrelines (the through-thickness amplitude follows a linear taper from the wrinkle interface plies down to zero at the laminate outer surfaces). The last two are single-wrinkle modes that swap that taper for a different through-thickness profile.

Morphology # wrinkles Phase φ Through-thickness amplitude M_f (compression) When to use
stack 2 0 Linear decay, 1 at interface → 0 at surfaces 1.0 (baseline) Two aligned wrinkles, peaks-over-peaks. The dual-wrinkle reference case used to scale convex / concave.
convex 2 +π/2 Linear decay, 1 at interface → 0 at surfaces < 1 Two phase-shifted wrinkles whose interface bulges outward. Least damaging dual-wrinkle case in compression.
concave 2 −π/2 Linear decay, 1 at interface → 0 at surfaces > 1 Two phase-shifted wrinkles whose interface pinches inward. Most damaging dual-wrinkle case in compression — design-driving.
uniform 1 n/a Full amplitude on every ply (no decay) 1.0 (no pairing) A single through-thickness-wide wrinkle — every ply wavy with the same A. Conservative bound and sanity-check baseline.
graded 1 n/a Linear decay from mid-ply to surfaces, with floor decay_floor ∈ [0, 1] 1.0 (no pairing) An embedded wrinkle that fades toward the surface plies. decay_floor=0 is pure graded; decay_floor=1 collapses to uniform.

stack vs uniform — what's the difference?

These two get conflated because both have M_f = 1.0, but they model very different defects:

  • stack places two wrinkles at adjacent interfaces with φ = 0 (aligned crests). Through the thickness the wrinkle decays linearly from the interface plies to zero at the outer surfaces — surface plies are flat.
  • uniform places a single wrinkle and disables the through-thickness decay — every ply, including the outer surfaces, is displaced by the full profile.

For the same amplitude / wavelength, apply_to_nodes therefore produces different deformed meshes: stack has a wrinkle concentrated near the interface plies (and flat top/bottom plies), while uniform has a wrinkle of the same amplitude at every single ply. The M_f = 1.0 coincidence is purely the analytical knockdown parameter — the FE geometry, the per-ply fibre-angle field, and the predicted ply-by-ply failure are not the same.

Supported failure criteria

The criteria below live in src/wrinklefe/failure/ and can be selected through FailureEvaluator or used independently:

  • LaRC04/05 (larc05.py) — Pinho/Camanho 3-D criterion with fibre-kinking under compression, in-situ matrix strengths, and a fracture-plane search. Default for the FE solve.
  • Tsai-Wu (tsai_wu.py) — 3-D tensor-polynomial criterion with a configurable interaction coefficient.
  • Tsai-Hill (tsai_hill.py) — 3-D extension of the classical quadratic Tsai-Hill index.
  • Hashin (hashin.py) — 3-D Hashin criterion with separate fibre-tension/-compression and matrix-tension/-compression modes.
  • Puck (puck.py) — action-plane (Mode A/B/C) inter-fibre-failure criterion with simplified fibre failure.
  • Maximum Stress (max_stress.py) and Maximum Strain (max_strain.py) — non-interactive checks against the principal material-frame allowables.
  • Budiansky-Fleck kink-band (kinkband.py) — analytical compression knockdown with an optional interlaminar damage coupling (InterlaminarDamage); this is the model exposed in the analytical_knockdown field of AnalysisResults.
  • Progressive damage (progressive.py) — PlyDiscount and ContinuumDamage post-failure stiffness reduction models that wrap any of the criteria above.

How It Works

The full mechanism-by-mechanism derivation lives on the Theory: physics & mechanics page (docs/theory.md). The essentials:

Wrinkle kinematics

A wrinkle is reduced to its peak fibre-misalignment angle

theta_max = arctan(2*pi*A / lambda)

(half-amplitude A, wavelength λ) and — for unidirectional laminates — its through-thickness penetration D/T = A/T (T = laminate thickness). theta_eff = M_f * theta_max folds in the morphology factor M_f (stack = 1, convex < 1, concave > 1).

Compression — CLT-weighted Budiansky–Fleck kink-band

KD_lam      = f_0 * KD_BF + (1 - f_0)
KD_BF       = 1 / (1 + r + c_AF * r^2),   r = theta_eff / gamma_Y_eff
gamma_Y_eff = max(0.032 + 0.050 * f_confined
                        - 0.010 * max(n_block_max - 1, 0),  0.016)

f_0 is the axial-stiffness fraction carried by the 0° plies (the plies that kink); the (1 - f_0) term is the off-axis plies riding through at full strength. The matrix shear-yield strain gamma_Y_eff rises with the confinement f_confined (off-axis neighbours bracing the 0° plies against kink-band rotation) and falls with the longest run of consecutive 0° plies n_block_max (blocked 0° plies kink more easily), floored at half the UD value. So a dispersed [0/45/90/-45]s resists wrinkle knockdown far better than a blocked [0_4/90_4]s. The optional Argon–Fleck quadratic term c_AF (kink_band_quadratic_coeff) defaults to 0 — the pure linear Budiansky–Fleck floor.

Tension — three-mechanism minimum, CLT-weighted

KD_lam = f_0 * min(cos^2(theta), KD_matrix, KD_oop) + (1 - f_0)

The 0° ply knockdown is the most severe of three competing mechanisms: fibre load-rotation (cos^2(theta)), in-situ matrix cracking (a Hashin/LaRC σ22τ12 interaction with a thick-ply in-situ strength correction, KD_matrix), and a curved-beam out-of-plane delamination check (KD_oop: the wrinkle curvature drives an interlaminar σ33 at the crest and τ13 at the flanks). A Benzeggagh–Kenane mixed-mode delamination-onset knockdown is reported alongside, and the tension knockdown is floored by the compression value for the same defect ("tension is never worse than compression").

Graded morphology

For the graded morphology the knockdown is averaged over the wrinkle profile in both the longitudinal (x) and through-thickness (z) directions. The compression path weights each ply by a Gaussian through-thickness envelope centred at wrinkle_z_position (decay scale max(λ/2, A)); the tension path uses an analogous linear taper. In both, decay_floor sets the surface-ply amplitude: 0 is a fully embedded wrinkle that fades to flat at the surfaces, 1 collapses to uniform.

References

  • Elhajjar, R. (2025). Scientific Reports, 15:25977.
  • Li, Y. et al. (2026). Composites Part A, 205:109719.
  • Li, X. et al. (2024). Composites Science and Technology, 256:110762.
  • Li, Y. et al. (2025). Polymer Composites, 46:15176-15187.
  • Hsiao, H.M. & Daniel, I.M. (1996). Composites Science and Technology, 56(5), 581-593.
  • Budiansky, B. & Fleck, N.A. (1993). J. Mech. Phys. Solids, 41(1), 183-211.
  • Pinho, S.T. et al. (2005). NASA-TM-2005-213530.
  • Camanho, P.P. et al. (2006). Composites Part A, 37(2), 165-176.
  • Jin, L. et al. (2026). Thin-Walled Structures, 219:114237.

License

MIT - see LICENSE

Changelog

Notable changes between versions — including any that shift predictions, flagged under a Numerical results heading — are recorded in CHANGELOG.md.

Contributing

See CONTRIBUTING.md

Citation

If you use WrinkleFE in your research, please cite it. The quickest way is the "Cite this repository" button on the GitHub page — it's generated from CITATION.cff and exports APA or BibTeX. The full software citation:

Elhajjar, R. (2025). WrinkleFE: An open-source finite element package for strength prediction of wrinkled composite laminates (Version 1.0.0) [Computer software]. University of Wisconsin-Milwaukee. https://github.com/elhajjar1/WrinkleFE

@software{elhajjar2025wrinklefe,
  author = {Elhajjar, Rani},
  title = {{WrinkleFE}: An Open-Source Finite Element Package for Strength
           Prediction of Wrinkled Composite Laminates},
  year = {2025},
  version = {1.0.0},
  publisher = {GitHub},
  url = {https://github.com/elhajjar1/WrinkleFE},
  note = {University of Wisconsin-Milwaukee}
}

Please also cite the underlying experimental validation data:

Elhajjar, R. (2025). Fat-tailed failure strength distributions and manufacturing defects in advanced composites. Scientific Reports, 15, 25977. https://doi.org/10.1038/s41598-025-06693-4