Pumpkin Carving Stress: 3D Shell Analysis

Carve a Cutout

Pick a shape, then click anywhere on the pumpkin's curved shell to carve it there. Up to 6 cutouts.

Shell Physics

Rind thickness 8 mm

Turgor pressure 8.0 kPa

Corner sharpness 0.60

Stress Readout

Baseline shell stress

0 kPa

Peak concentration K_t

1.0×

Peak edge stress

0 kPa

Cutouts carved

0 / 6

Low (baseline membrane stress) → High (concentrated at sharp cutout corners)

How it works

A pumpkin rind behaves like a thin pressurized spherical shell: internal turgor pressure P stretches the curved wall into membrane tension, with baseline stress given by the standard thin-wall pressure-vessel formula:

σ_base = P·R / (2·t)     (R = shell radius, t = rind thickness)

Cutting an opening into that loaded shell — exactly like a hole in a pressurized aircraft fuselage or pipe — breaks the smooth stress path around it, forcing the load to detour around the edge and concentrate there. A circular hole in an infinite plate under tension carries the classic textbook factor K_t ≈ 3; sharper corners (triangles, zigzags) raise K_t further because stress must turn through a tighter radius, and the concentration falls off away from the edge over a bending decay length L ≈ √(R·t).

Rind thickness — a thinner shell carries more stress for the same pressure and load, per σ_base = P·R/2t.
Turgor pressure — the internal pressure driving the baseline membrane tension before any cutting.
Corner sharpness — rounds or sharpens every cutout's corners; sharper corners raise the local stress-concentration factor K_t, exactly as a fillet radius does at a real structural cutout.

Real-world relevance: this is why a carved jack-o'-lantern collapses fastest at its sharpest triangle-eye corners, and why engineers round cutout corners on pressurized shells, fuselage windows and pipe branches instead of leaving square or pointed edges.

drag = orbit · click pumpkin = carve

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