forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
7a69fe5e2f
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 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
45 lines
1.5 KiB
JSON
45 lines
1.5 KiB
JSON
{
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"title": "Bauschinger effect of linear kinematic hardening: tension, then back to zero strain",
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"kind": "theory",
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"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)",
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"quantities": [
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{
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"id": "residual_stress",
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"quantity": "axial stress back at zero strain after a pull to ε_a = 0.01",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Pull",
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"elements": [
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1
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]
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},
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"pointer": "/elements/0/stress/0/0"
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},
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"value": -247.52475247524754,
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"tolerance": {
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"relative": 1e-06
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},
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"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)"
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},
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{
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"id": "plastic_strain",
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"quantity": "accumulated equivalent plastic strain",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Pull",
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"elements": [
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1
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]
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},
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"pointer": "/elements/0/plastic_strain/0"
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},
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"value": 0.016089108910891083,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "(σ_a − σ_y)/H forward plus E/(E + H) (ε_a − 2σ_y/E) in reverse"
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}
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]
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} |