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
9 lines
613 B
Markdown
9 lines
613 B
Markdown
# A heated bar held at its ends past yield
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A steel bar 4 × 1 × 1 of 4 hex8 elements (E = 200000, ν = 0.3, σ_y = 250, H = 2000 isotropic,
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α = 1.2·10⁻⁵ from 20 degrees) on symmetry planes at x = 0, y = 0, z = 0 and held at x = 4 (its
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axial strain is zero; the lateral faces are free), heated uniformly to 320 by a temperature load
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in a nonlinear static step without nonlinear geometry. The mechanical strain is −α ΔT = −0.0036,
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2.9 times the yield strain, so the bar yields in compression: σ = −(σ_y + E_t (α ΔT − σ_y/E)) =
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−254.653 with E_t = E H/(E + H), and ε_p = (|σ| − σ_y)/H.
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