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 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
15 lines
746 B
Markdown
15 lines
746 B
Markdown
# Mooney–Rivlin block in Treloar's three modes
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One hybrid hex20 unit cube on three symmetry planes, E = 3, ν = 0.49 (μ = 1.006711,
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κ = 50), Mooney–Rivlin with C₀₁ = 0.2 (C₁₀ = μ/2 − C₀₁ = 0.303356), in three nonlinear
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static steps:
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- **Uniaxial**: the face x = 1 pulled to λ = 2, the others free.
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- **Equibiaxial**: x = 1 and y = 1 pulled to λ = 1.5, z free.
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- **Pure shear**: x = 1 pulled to λ = 2, y = 1 held (λ_y = 1), z free.
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The references are the compressible decoupled energy's principal Cauchy stresses
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σᵢ = (λᵢ/J) ∂W/∂λᵢ, by differences of W alone, with the free stretch found by bisection so the
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free faces carry no stress. The deformation is homogeneous, so the element represents it
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exactly.
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