forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
9ba6224bb7
nl-hybrid-incompressible: 27 hybrid hex8 at ν = 0.4999 pulled to λ = 2 by a prescribed displacement, against the compressible neo-Hookean closed form (1.4·10⁻⁹); its first iterations need the LDLᵀ factorization. ROADMAP and parity updated, docs/oracle.md regenerated. Co-Authored-By: Claude Opus 5.5 <[email protected]>
53 lines
1.6 KiB
JSON
53 lines
1.6 KiB
JSON
{
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"title": "Nearly incompressible hybrid block under prescribed stretch",
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"kind": "theory",
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"source": "Uniaxial stress of the decoupled compressible neo-Hookean energy W = μ/2 (Ī₁ − 3) + κ/2 (J − 1)² (P. J. Flory, Trans. Faraday Soc. 57:829–838, 1961): σ = μ J^(−5/3) (λ² − I₁/3) + κ (J − 1) with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.4999: μ = 1.0000667, κ = 5000)",
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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, ν = 0.4999",
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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": 3.498756466061613,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): 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": -0.29281075714096483,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): the tolerance admits the Newton tolerance and rounding"
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}
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]
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} |