forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
d586d84859
Five cases against closed forms: a Mooney-Rivlin block in Treloar's uniaxial, equibiaxial and pure-shear modes and a Yeoh block in uniaxial tension (the compressible energy's stresses, exact); a stretched Mooney-Rivlin tube inflated by a follower pressure (Rivlin's incompressible solution, 0.6 % at nu = 0.4995); free and fully held thermal expansion at a thermal stretch of 1.2 (exact); a bar held at its ends heated past yield (exact). docs/fem.md, the literature, ROADMAP (M15, M17), parity and the oracle page follow. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
11 lines
773 B
Markdown
11 lines
773 B
Markdown
# Inflation of a stretched Mooney–Rivlin tube
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The quarter tube of `nl-cylinder-inflation` (A = 10, B = 20, one unit long, 6 × 16 hybrid
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hex20), now Mooney–Rivlin (E = 3, ν = 0.4995, so μ = 1.000333; C₀₁ = 0.2, C₁₀ = μ/2 − C₀₁) and
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stretched axially by its end face (u_z = 0.5 at z = 1: λ_z = 1.5) while a follower pressure
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p = 0.540850 inflates the bore. In plane strain (λ_z = 1) Mooney–Rivlin is neo-Hookean with
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μ = 2(C₁₀ + C₀₁), since Ī₁ = Ī₂ there; the axial stretch makes the second invariant's share
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count: σ_θ − σ_r = 2(λ_θ² − λ_r²)(C₁₀ + C₀₁ λ_z²). Integrated through the incompressible wall,
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r² = a² + (R² − A²)/λ_z, that pressure puts the bore at a = 15 and the outer wall at
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b = 20.615528.
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