[andreachiocca]

Follows #56 (merged); the diff now contains only this step.

Preview (available once the preview check succeeds):

• FIG. R02.2, chapter 01: https://pr-57.academic-website-preview.pages.dev/research/#multifat-comparison
• Italian version: https://pr-57.academic-website-preview.pages.dev/it/research/#multifat-comparison

1. FIG. R02.2: criteria compared (step 5b)

A matrix of 38 multiaxial fatigue criteria × 6 materials with life data, produced by multifat-pipeline --all (multiaxial-fatigue 67f06ea). The caption presents it as the open benchmark of the multifat library, regenerated whenever the library changes.

Rows are the criteria, grouped by family: critical plane, invariant, integral, energy.

Columns are the materials, ordered by number of tests:

• Al7075-T6
• Ti6Al4V Berto
• 42CrMo4 QT
• AISI316L
• 42CrMo4 Reis
• Ti6Al4V

Metric. The load-equivalent error is $e_L=\ln(1/s^\ast)$, where $s^\ast$ scales the load history until the calibrated criterion predicts the observed life (multifat.eval.load_error).

Two views:

• share of tests within ±10 % of the load;
• mean $e_L$ on a diverging scale, where amber is non-conservative and teal is conservative.

Interaction. Hovering a cell, or moving with the arrow keys, shows the criterion (with its DOI), its complexity facets, n, the shares within ±10/±20 % and the mean $e_L$ ± SD.

What $e_L$ measures

The caption has a disclosure, in EN and IT, that explains:

• the definition of $s^\ast$ and $e_L$;
• the sign convention, with a worked example: $e_L=+0.10$ means a match only at about 0.90 × the load, i.e. conservative;
• why the load scale is independent of the S–N slope and of the degree of the damage parameter;
• the within-band shares, bias and scatter;
• what is counted;
• the open independence caveat from multifat issue Update academic profile, publications and FABER research outputs #14.

Complexity shown beside the score

Three facets are read from the multifat registry; none of them is a computed score:

• the inputs: stress only, or stress and strain ($E,\nu$);
• the life law: calibrated master curve $DP=A,N^b$, or the criterion's own law;
• the declared material constants, with optional ones marked *.

The matrix shows the first two as dot columns ε and N; the readout lists all three. The composite ranking KPI is proposed in andreachiocca/multiaxial-fatigue#57 and belongs to multifat; the site will draw it once multifat computes it.

What is counted

Only assessment observations (Flag = 1, failures not used for calibration). Not counted:

• design points;
• run-outs;
• the seven workbooks that contain only fatigue limits.

Cells marked not applicable are combinations the pipeline does not run. RFB, for example, falls outside its validity range $0.577<t_{-1}/s_{-1}<0.866$ on GGG60 and AISI316L.

Generator and tests

scripts/generate_multifat_comparison.py only collects the pipeline outputs:

• Comparison/summary_error_stats_by_role.csv;
• comparison_capabilities.csv;
• the registry.

tests/test_multifat_comparison.py checks:

• the pin;
• that the metric is Error_load restricted to assessment observations;
• the families;
• that each share is k/n with within10 ≤ within20;
• that $|\bar e_L|\le\ln(1/0.9)$ whenever every test is within ±10 %;
• that the complexity facets are declared and no score is present;
• the chapter binding and the i18n keys.

2. Figures always up to date

• _data/figure_sources.yml: one pinned commit per figure (T01, R02.1, R02.2, R03.1). Includes read the commit from this file, and each test checks that it matches its JSON.
• scripts/refresh_figures.py: compares each pin with the HEAD of the source repository. When the source has moved, it clones it, installs it, reruns that figure's generator and updates the pin.
• .github/workflows/refresh-figures.yml:
  • runs every Monday, plus workflow_dispatch (with force) and repository_dispatch (research-code-updated);
  • regenerates the figures and runs the unit tests;
  • opens or updates the automation/refresh-figures PR;
  • dispatches build.yml and preview.yml itself, because PRs opened with GITHUB_TOKEN trigger no workflows.
• Tested locally end to end on T01: 5cd5124 → 67f06ea. Only the provenance changes; the values are identical.

3. Other changes

• Research chapters take a figures list in _data/research_areas.json, so chapter 01 holds R02.1 and R02.2.
• CLAUDE.md and docs/site-roadmap.md are updated.

Verification (local)

• unittest passes.
• Ruby checks pass.
• Production build and all page verifiers pass.
• Browser checks match the master baseline (CDN errors from this environment).
• Screenshots checked at 1280 and 375 px, EN and IT.

🤖 Generated with Claude Code

https://claude.ai/code/session_01KzHgFgeEYmpqcsxvvbphUy