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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
54 lines
1.5 KiB
JSON
54 lines
1.5 KiB
JSON
{
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"title": "Uniaxial stretch of a neo-Hookean block to twice its length",
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"kind": "theory",
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"source": "Closed form of the compressible neo-Hookean model W = μ/2 (Ī₁ − 3) + κ/2 (J − 1)² in uniaxial stress (G. A. Holzapfel, Nonlinear Solid Mechanics, Wiley 2000, §6.5, eq. 6.148 with the volumetric term of §6.4): σ_yy = μ J^(−5/3)(l² − Ī/3) + κ(J − 1) = 0 fixes the lateral stretch l, then σ_xx = μ J^(−5/3)(λ² − l²)",
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"quantities": [
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{
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"id": "sigma",
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"quantity": "axial Cauchy stress at the corner (1, 1, 1), 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": "Stretch",
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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": 8.060135422196785,
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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 element represents exactly: the tolerance only admits rounding and the Newton tolerance"
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},
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{
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"id": "lateral",
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"quantity": "lateral displacement u_y at the corner (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": "Stretch",
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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": -0.1868562805727787,
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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 element represents exactly: the tolerance only admits rounding and the Newton tolerance"
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}
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]
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}
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