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
604 B
Markdown
9 lines
604 B
Markdown
# Free and constrained thermal expansion at finite strain
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A unit cube of 2 × 2 × 2 hex20, compressible neo-Hookean (E = 10, ν = 0.3) with an expansion
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coefficient α = 10⁻³ from 20 degrees, heated to 220 by a temperature load in two nonlinear static
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steps: **Free** (three symmetry planes) and **Held** (symmetry planes on all six faces). The
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thermal stretch is ϑ = 1 + α ΔT = 1.2. Free, the cube grows to 1.2 along every edge without
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stress; held, F = I, the material's mechanical part is F_m = ϑ⁻¹ I and its stress the neo-Hookean
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pressure κ (J_m − 1) with J_m = ϑ⁻³: −3.510802.
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