forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
8ca2dddeec
Theory cases for the nonlinear solver, each frozen as a fixture: uniaxial stretch of a neo-Hookean block to twice its length (closed form), the nonlinear patch test on a distorted hex8 mesh, a quarter turn of the same mesh (objectivity: zero stress), the elastica of a hex20 cantilever at P L²/(E I) = 1, 2, 5, 10 against Bisshopp–Drucker (0.2–0.5 %), and the inflation of a thick neo-Hookean tube by a follower pressure against Rivlin's closed form (0.08 % at the bore). A finite-strain Cook's membrane is pending its transcribed reference. docs/fem.md describes the formulation, the material point interface, the follower-pressure choice and what nonlinear steps refuse; the literature, parity and roadmap pages follow. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
54 lines
1.6 KiB
JSON
54 lines
1.6 KiB
JSON
{
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"title": "Inflation of a thick neo-Hookean cylinder by a follower pressure (plane strain)",
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"kind": "theory",
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"source": "Finite inflation of an incompressible neo-Hookean thick-walled tube in plane strain: r² = R² + a² − A², σ_θ − σ_r = μ (λ² − λ⁻²) with λ = r/R, integrated through the wall: p = (μ/2)[(ln λ_a² − λ_a⁻²) − (ln λ_b² − λ_b⁻²)] (R. S. Rivlin, Large elastic deformations of isotropic materials VI, Phil. Trans. R. Soc. A 242:173–195, 1949; R. W. Ogden, Non-Linear Elastic Deformations, Dover 1997, §5.3.2)",
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"quantities": [
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{
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"id": "ua",
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"quantity": "radial displacement of the bore (10, 0, 0) at the pressure that inflates it to a = 15",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Inflate",
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"at": [
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[
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10.0,
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0,
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0
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]
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]
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},
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"pointer": "/nodes/0/displacement/0"
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},
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"value": 5.0,
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"tolerance": {
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"relative": 0.005
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},
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"reason": "the closed form is incompressible and our material nearly so (κ/μ = 1000, a volume change of order p/κ ≈ 4·10⁻⁴); hybrid hex20, 6 × 16, follow the wall's strain gradient well inside"
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},
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{
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"id": "ub",
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"quantity": "radial displacement of the outer wall (20, 0, 0)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Inflate",
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"at": [
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[
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20.0,
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0,
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0
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]
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]
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},
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"pointer": "/nodes/0/displacement/0"
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},
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"value": 2.9128784747791983,
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"tolerance": {
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"relative": 0.005
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},
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"reason": "as at the bore"
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}
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]
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}
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