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 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
45 lines
1.2 KiB
JSON
45 lines
1.2 KiB
JSON
{
|
||
"title": "A steel bar held at its ends and heated past yield (small strain)",
|
||
"kind": "theory",
|
||
"source": "Uniaxial J2 plasticity with linear hardening (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) with the additive thermal strain: the bar's total axial strain is held at zero, so its mechanical strain is −α ΔT and σ = −(σ_y + E_t (α ΔT − σ_y/E)) once α ΔT exceeds σ_y/E",
|
||
"quantities": [
|
||
{
|
||
"id": "sigma",
|
||
"quantity": "axial stress, ΔT = 300 (α ΔT = 3.6·10⁻³, 2.9 times the yield strain)",
|
||
"measure": {
|
||
"command": "solve.probe",
|
||
"params": {
|
||
"step": "Heat",
|
||
"elements": [
|
||
2
|
||
]
|
||
},
|
||
"pointer": "/elements/0/stress/0/0"
|
||
},
|
||
"value": -254.65346534653466,
|
||
"tolerance": {
|
||
"relative": 1e-08
|
||
},
|
||
"reason": "a homogeneous uniaxial state the elements represent exactly"
|
||
},
|
||
{
|
||
"id": "plastic_strain",
|
||
"quantity": "equivalent plastic strain",
|
||
"measure": {
|
||
"command": "solve.probe",
|
||
"params": {
|
||
"step": "Heat",
|
||
"elements": [
|
||
2
|
||
]
|
||
},
|
||
"pointer": "/elements/0/plastic_strain/0"
|
||
},
|
||
"value": 0.0023267326732673297,
|
||
"tolerance": {
|
||
"relative": 1e-07
|
||
},
|
||
"reason": "(|σ| − σ_y)/H, as for the stress"
|
||
}
|
||
]
|
||
} |