verification: implicit plasticity oracle cases and documentation

Four cases, each against its closed form: uniaxial tension of a J2 cube to a
logarithmic strain of 0.2 (Kirchhoff stress exact; 0.13 % from the explicit
solver's hypoelastic Cauchy stress, the elastic volume change between the two
laws), the Bauschinger effect of linear kinematic hardening on a load path
back to zero strain (exact), Hill's elastic-perfectly plastic thick cylinder
(bore displacement at a plastic radius of 1.5a within 0.009 %, collapse
pressure within 2e-8; the pending case is now active) and a cantilever's
plastic collapse, converged 3.1 % above beam theory's hinge, the bound a
continuum exceeds. docs/fem.md, the literature, ROADMAP (M15), parity and the
oracle page follow.

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 2026-10-14 06:03:36 -04:00
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{
"title": "Uniaxial tension of a J2 bilinear-hardening cube to large strain (implicit, finite strain)",
"kind": "theory",
"source": "J2 plasticity with linear isotropic hardening in uniaxial stress (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) in the logarithmic strain, which Simo's exponential return map (CMAME 99:61–112, 1992) integrates exactly on a proportional path: Kirchhoff stress τ = σ_y + E_t (ε − σ_y/E), Cauchy stress σ = τ/J with ln J = τ/(3K) (Hencky's volume law)",
"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/0/0"
},
"value": 642.7365391418857,
"tolerance": {
"relative": 1e-06
},
"reason": "a homogeneous deformation the element represents exactly, reached on a proportional path: the tolerance only admits the Newton tolerance and rounding"
},
{
"id": "plastic_strain",
"quantity": "equivalent plastic strain",
"measure": {
"command": "solve.probe",
"params": {
"step": "Pull",
"elements": [
1
]
},
"pointer": "/elements/0/plastic_strain/0"
},
"value": 0.19678217821782182,
"tolerance": {
"relative": 1e-06
},
"reason": "ε_p = (τ − σ_y)/H, as for the stress"
}
]
}