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
This commit is contained in:
jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 06:03:36 -04:00
1 parent 17b2c837f2
commit 7a69fe5e2f
21 files changed
+414 -25

No files matched your search

+45
View File
@@ -0,0 +1,45 @@
{
"title": "Bauschinger effect of linear kinematic hardening: tension, then back to zero strain",
"kind": "theory",
"source": "J2 plasticity with Prager's linear kinematic hardening in uniaxial stress (W. Prager, Ing.-Arch. 1955; Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3): from σ_a = σ_y + E_t (ε_a − σ_y/E) the material unloads elastically by 2σ_y and then hardens with E_t, so at zero strain σ = σ_a − 2σ_y − E_t (ε_a − 2σ_y/E)",
"quantities": [
{
"id": "residual_stress",
"quantity": "axial stress back at zero strain after a pull to ε_a = 0.01",
"measure": {
"command": "solve.probe",
"params": {
"step": "Pull",
"elements": [
1
]
},
"pointer": "/elements/0/stress/0/0"
},
"value": -247.52475247524754,
"tolerance": {
"relative": 1e-06
},
"reason": "a homogeneous small-strain state the element represents exactly, with increments that end at the load path's turn; isotropic hardening would give −281.835 (it yields again only at −σ_a)"
},
{
"id": "plastic_strain",
"quantity": "accumulated equivalent plastic strain",
"measure": {
"command": "solve.probe",
"params": {
"step": "Pull",
"elements": [
1
]
},
"pointer": "/elements/0/plastic_strain/0"
},
"value": 0.016089108910891083,
"tolerance": {
"relative": 1e-06
},
"reason": "(σ_a − σ_y)/H forward plus E/(E + H) (ε_a − 2σ_y/E) in reverse"
}
]
}