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
53 lines
1.4 KiB
JSON
53 lines
1.4 KiB
JSON
{
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"title": "Yeoh block in uniaxial tension",
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"kind": "theory",
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"source": "Uniaxial tension of the decoupled compressible Yeoh energy W = C₁₀ (Ī₁ − 3) + C₂₀ (Ī₁ − 3)² + C₃₀ (Ī₁ − 3)³ + κ/2 (J − 1)² (O. H. Yeoh, Rubber Chem. Technol. 66(5):754–771, 1993): σ = (λ/J) ∂W/∂λ with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.49, C₁₀ = μ/2, C₂₀ = −0.02, C₃₀ = 0.004)",
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"quantities": [
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{
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"id": "sigma",
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"quantity": "axial Cauchy stress, stretch λ = 2",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Uniaxial",
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"at": [
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[
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1,
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1,
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1
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]
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]
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},
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"pointer": "/nodes/0/stress/0"
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},
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"value": 3.174263919393508,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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},
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{
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"id": "lateral",
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"quantity": "lateral displacement at (1, 1, 1): l − 1",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Uniaxial",
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"at": [
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[
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1,
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1,
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1
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]
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]
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},
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"pointer": "/nodes/0/displacement/1"
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},
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"value": -0.2854505757255106,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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}
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]
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} |