oracle: 2D cases (Kirsch plane stress, Lamé plane strain and axisymmetric, rotating disc and cylinder, NAFEMS LE1 with quad8) and J2 uniaxial explicit

The pending 2D LE1 case becomes a real one; the plasticity cases stay
pending with what they still need (static J2 for the collapse pressure,
the transcribed measurements for the Taylor bar).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-13 21:42:19 -04:00
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{
"title": "Uniaxial tension of a J2 bilinear-hardening cube to large strain (explicit)",
"kind": "theory",
"source": "von Mises plasticity with linear isotropic hardening under uniaxial stress (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3); logarithmic strain for a hypoelastic–plastic law under coaxial stretching",
"quantities": [
{
"id": "sigma",
"quantity": "axial Cauchy stress at a logarithmic strain of 0.2",
"measure": {
"command": "solve.probe",
"params": {
"step": "Pull",
"elements": [
1
]
},
"pointer": "/elements/0/stress/0"
},
"value": 643.5643564356436,
"tolerance": {
"relative": 0.01
},
"reason": "uniaxial J2 with linear hardening: σ = σ_y + E_t (ε − σ_y/E) in logarithmic strain; the stretch takes 10⁴ wave transits, so inertia and the ringing of the start (ρcv ≈ 0.1% of σ) stay well under 1%"
},
{
"id": "plastic_strain",
"quantity": "equivalent plastic strain",
"measure": {
"command": "solve.probe",
"params": {
"step": "Pull",
"elements": [
1
]
},
"pointer": "/elements/0/plastic_strain"
},
"value": 0.1967821782178218,
"tolerance": {
"relative": 0.01
},
"reason": "ε_p = ε − σ/E, as for the stress"
}
]
}