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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
76 lines
1.7 KiB
JSON
76 lines
1.7 KiB
JSON
{
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"title": "Free and fully constrained thermal expansion at finite strain",
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"kind": "theory",
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"source": "The multiplicative split F = F_m F_θ with F_θ = (1 + α ΔT) I (V. A. Lubarda, Appl. Mech. Rev. 57(2):95–108, 2004): a free body follows F = F_θ stress-free; held on every face, F = I and F_m = ϑ⁻¹ I, so the compressible neo-Hookean material carries the pressure of its volume ratio, σ = κ (ϑ⁻³ − 1)",
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"quantities": [
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{
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"id": "free_u",
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"quantity": "displacement of the corner (1, 1, 1) along x, free, α ΔT = 0.2",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Free",
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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/0"
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},
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"value": 0.2,
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"tolerance": {
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"relative": 1e-08
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},
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"reason": "a homogeneous stretch every element represents exactly"
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},
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{
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"id": "free_stress",
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"quantity": "stress of the free body (σ_xx at the corner)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Free",
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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": 0.0,
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"tolerance": {
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"absolute": 1e-08
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},
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"reason": "rounding only"
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},
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{
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"id": "held_stress",
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"quantity": "stress of the held block, σ_xx (hydrostatic)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Held",
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"at": [
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[
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0.5,
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0.5,
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0.5
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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": -3.5108024691358017,
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"tolerance": {
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"relative": 1e-08
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},
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"reason": "a homogeneous state; E = 10, ν = 0.3 (κ = 8.3333), ϑ = 1.2"
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}
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]
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} |