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
122 lines
3.1 KiB
JSON
122 lines
3.1 KiB
JSON
{
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"title": "Mooney–Rivlin block in uniaxial, equibiaxial and pure-shear tension",
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"kind": "theory",
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"source": "Treloar's homogeneous modes of rubber testing (L. R. G. Treloar, The Physics of Rubber Elasticity, 3rd ed., Oxford 1975, ch. 10) for the decoupled compressible energy W = C₁₀ (Ī₁ − 3) + C₀₁ (Ī₂ − 3) + κ/2 (J − 1)²: principal Cauchy stresses σᵢ = (λᵢ/J) ∂W/∂λᵢ with the free stretch found so the free faces carry no stress (bisection; E = 3, ν = 0.49, C₀₁ = 0.2, C₁₀ = μ/2 − C₀₁)",
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"quantities": [
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{
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"id": "uniaxial",
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"quantity": "axial Cauchy stress, uniaxial stretch λ = 2",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Uniaxial",
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"at": [
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},
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"pointer": "/nodes/0/stress/0"
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},
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"value": 2.736633402084229,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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},
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{
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"id": "uniaxial_lateral",
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"quantity": "lateral displacement at (1, 1, 1), uniaxial: l − 1",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Uniaxial",
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"at": [
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]
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},
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"pointer": "/nodes/0/displacement/1"
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},
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"value": -0.28647206688129256,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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},
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{
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"id": "equibiaxial",
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"quantity": "in-plane Cauchy stress, equibiaxial stretch λ = 1.5",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Equibiaxial",
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"at": [
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},
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"pointer": "/nodes/0/stress/0"
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},
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"value": 2.842734818108988,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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},
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{
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"id": "shear_xx",
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"quantity": "Cauchy stress along the stretch, pure shear λ = 2",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Shear",
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"at": [
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},
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"pointer": "/nodes/0/stress/0"
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},
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"value": 3.526124960232999,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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},
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{
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"id": "shear_yy",
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"quantity": "Cauchy stress across, in the held direction, pure shear λ = 2",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Shear",
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"at": [
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]
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},
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"pointer": "/nodes/0/stress/1"
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},
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"value": 1.506681177907714,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding"
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}
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]
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} |