[andreachiocca]

Preview (once the preview check succeeds): https://pr-49.academic-website-preview.pages.dev/research/#critical-plane-explorer · IT: https://pr-49.academic-website-preview.pages.dev/it/research/#critical-plane-explorer

Prototype of Step 5a in docs/site-roadmap.md: the first figure generated from the original research code. Independent of #47 and #48.

What it shows

Each point of a sphere is a material plane, identified by its normal $\mathbf n$; $\mathbf n$ and $-\mathbf n$ are the same plane, so the data cover a hemisphere. The colour is the Findley damage parameter $D/\sigma_a$ for

$$\sigma_{xx}=\sigma_a\sin\omega t,\qquad \tau_{xy}=\lambda,\sigma_a\sin(\omega t-\Delta\varphi),\qquad \text{zero mean},$$

with $\lambda\in{0,0.25,0.5,0.75,1}$ and $\Delta\varphi\in{0,15,\dots,90^\circ}$. Planes within 1.5 % of the maximum are shown in amber, and the arrow marks one critical normal $\mathbf n^\ast$.

How it is computed

• scripts/generate_damage_sphere.py calls multifat.models.cp_methods.fin_harmonic.evaluate_findley (MCC shear amplitude) once per plane. The plane frames come from multifat.planes.sampling.gentang, on a 3° grid (3720 planes × 35 cases, about 30 s). The library's own search over the same grid is asserted to give the same maximum.
• Pinned at multiaxial-fatigue@5cd5124362c02fe83ec40ffa8bf93e4d12ccc782. The output is assets/data/figures/damage-sphere-findley.json (174 kB: uint8 field plus exact per-case maxima and normals), with provenance metadata and a SHA-256 of the payload.
• The browser only draws the stored grid with bilinear interpolation; no fatigue criterion is reimplemented in JavaScript.
• $k = 0.3$ is illustrative, and the caption says so.

Scientific checks (tests/test_damage_sphere.py)

• Uniaxial: $D^\ast/\sigma_a=\tfrac12\left(k+\sqrt{1+k^2}\right)=0.6720$. The critical planes form a cone at $\tfrac12\arctan(1/k)=36.65^\circ$ from the load axis (grid: 36.4°).
• In-phase: $D^\ast/\sigma_a=k/2+\sqrt{1/4+\lambda^2}\sqrt{1+k^2}$ for all $\lambda$, within 2·10⁻³.
• $\Delta\varphi=90^\circ$: $D^\ast\ge(\lambda+k),\sigma_a$ (the plane normal to $x$), with equality for $\lambda\ge0.5$.
• Payload integrity and provenance (the commit shown in the caption equals the data's).

Interaction and motion

• Sliders for $\lambda$ and $\Delta\varphi$ with a 320 ms eased transition between cases.
• Drag or arrow keys rotate the sphere.
• A slow automatic spin can be paused with a button; it is off with prefers-reduced-motion and stops when the figure leaves the viewport.
• Hover readout, live region with $D^\ast/\sigma_a$ and $\mathbf n^\ast$, and a bilingual caption with links to the data, the generator and the library commit.

Verification (local)

• unittest: 63 tests passed.
• Ruby checks: passed.
• Jekyll production build: OK.
• All page verifiers: passed.
• Browser checks: same result as the master baseline in this sandbox.
• Widget readouts match the generator (0.868 / 0.672 / 1.300 for the three cases tested).

Not in CI: regenerating the data needs multifat installed. CI checks the committed data instead.

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Generated by Claude Code