forked from 1b-agent/fieldcraft-upstream
oracle: filleted L-bracket on the octree all-hex mesh
A slow theory case: the corpus bracket meshed by mesh.hex.octree at 7, 5 and 4 mm, clamped at the base and loaded by 2 kN. Checks equilibrium, that every element is certified valid, the mesh volume against the CAD volume, the beam bending stress of the upright leg (sigma = M c / I = 145.3 MPa, within 5%) and the convergence of the fillet von Mises stress against the 4 mm mesh. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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@@ -2,7 +2,7 @@
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Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the policy is [verification.md](verification.md). Every case is our own model, built with FieldCraft commands from the problem's published description, and compared with the reference value its `expected.json` cites, within the stated tolerance and for the stated reason. Accepted results are frozen in each case's `fixture.json`: a later change that moves one beyond its band (10⁻⁹ of its size) fails CI even while the reference still passes. No reference value was produced with a commercial product.
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**163 of 169 quantities pass** (6 known failure(s)) in 49 active cases: 40 theory, 9 published benchmark, 0 experiment; 9 pending cases wait for capabilities still being built.
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**170 of 176 quantities pass** (6 known failure(s)) in 50 active cases: 41 theory, 9 published benchmark, 0 experiment; 9 pending cases wait for capabilities still being built.
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## Theory: closed-form solutions, patch tests and mesh invariants
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@@ -90,6 +90,13 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
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| [nl-thermal-expansion](../tests/oracle/nl-thermal-expansion/) | stress of the held block, σ_xx (hydrostatic) | -3.5108 | -3.5108 | < 1e-7% | 1e-8 rel. | pass | matches |
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| [nl-yeoh-uniaxial](../tests/oracle/nl-yeoh-uniaxial/) | axial Cauchy stress, stretch λ = 2 | 3.1743 | 3.1743 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-yeoh-uniaxial](../tests/oracle/nl-yeoh-uniaxial/) | lateral displacement at (1, 1, 1): l − 1 | -0.28545 | -0.28545 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | x reaction on the clamped face (5 mm mesh) | -2000 | -2000 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | elements the certified Jacobian check does not prove valid (5 mm mesh) | 0 | 0 | ≈ 0 | exact | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | mesh volume against the CAD volume (5 mm mesh) | 32145 | 32177 | 0.1% | 0.3% | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | σ_yy on the outer face of the upright leg at y = 19, z = 6 (5 mm mesh) | 145.31 | 149.26 | 2.72% | 5% | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | σ_yy on the inner face of the upright leg at y = 19, z = 6 (5 mm mesh) | -145.31 | -147.28 | -1.35% | 5% | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | von Mises stress at the middle of the fillet, 7 mm mesh | 143.21 | 138.53 | -3.27% | 5% | pass | matches |
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| [octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/) | von Mises stress at the middle of the fillet, 5 mm mesh | 143.21 | 144.53 | 0.921% | 2% | pass | matches |
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| [patch-hex20](../tests/oracle/patch-hex20/) | u_x at the corner (1, 1, 1) | -2.5000e-4 | -2.5000e-4 | < 1e-7% | 1e-9 rel. | pass | matches |
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| [patch-hex20](../tests/oracle/patch-hex20/) | u_y at the corner (1, 1, 1) | 0.001 | 0.001 | < 1e-7% | 1e-9 rel. | pass | matches |
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| [patch-hex20](../tests/oracle/patch-hex20/) | u_z at the corner (1, 1, 1) | 0.00225 | 0.00225 | < 1e-7% | 1e-9 rel. | pass | matches |
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@@ -220,6 +227,7 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
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- **[nl-rigid-rotation](../tests/oracle/nl-rigid-rotation/)** (theory): A quarter turn strains and stresses nothing (objectivity). Source: Objectivity of the total Lagrangian formulation and of the hyperelastic stress: a rigid motion x = R X + c gives C = I and σ = 0 whatever the rotation (Bonet & Wood 2008, §3.4 and §5.2; T. Belytschko, W. K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, 2nd ed., Wiley 2014, §5.5). Tolerances — ux: the inner nodes follow the rigid rotation exactly; uy: the inner nodes follow the rigid rotation exactly; uz: the inner nodes follow the rigid rotation exactly; von_mises: zero up to rounding of stresses of order E = 1000: a 90° turn leaves no strain
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- **[nl-thermal-expansion](../tests/oracle/nl-thermal-expansion/)** (theory): Free and fully constrained thermal expansion at finite strain. Source: The multiplicative split F = F_m F_θ with F_θ = (1 + α ΔT) I (V. A. Lubarda, Appl. Mech. Rev. 57(2):95–108, 2004): a free body follows F = F_θ stress-free; held on every face, F = I and F_m = ϑ⁻¹ I, so the compressible neo-Hookean material carries the pressure of its volume ratio, σ = κ (ϑ⁻³ − 1). Tolerances — free_u: a homogeneous stretch every element represents exactly; free_stress: rounding only; held_stress: a homogeneous state; E = 10, ν = 0.3 (κ = 8.3333), ϑ = 1.2
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- **[nl-yeoh-uniaxial](../tests/oracle/nl-yeoh-uniaxial/)** (theory): Yeoh block in uniaxial tension. Source: Uniaxial tension of the decoupled compressible Yeoh energy W = C₁₀ (Ī₁ − 3) + C₂₀ (Ī₁ − 3)² + C₃₀ (Ī₁ − 3)³ + κ/2 (J − 1)² (O. H. Yeoh, Rubber Chem. Technol. 66(5):754–771, 1993): σ = (λ/J) ∂W/∂λ with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.49, C₁₀ = μ/2, C₂₀ = −0.02, C₃₀ = 0.004). Tolerances — sigma: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding; lateral: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding
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- **[octree-filleted-bracket](../tests/oracle/octree-filleted-bracket/)** (theory): Filleted L-bracket on the octree all-hex mesh: equilibrium, beam bending, fillet stress convergence. Source: equilibrium; Euler–Bernoulli bending of the 8 × 40 mm leg, σ = M c / I with M = F (50 − y) (S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed., 1970, §102); grid convergence of the fillet stress against the 4 mm mesh of this case (P. J. Roache, Verification and Validation in Computational Science and Engineering, 1998, ch. 5). Tolerances — reaction_x: the reactions balance the 2 kN load to solver precision; invalid: the octree mesher returns only elements proven valid; volume: bilinear boundary faces on the R6 fillet and the two Ø8 holes, and the 1e-3 chordal tessellation they are fitted to; syy_outer: beam theory ignores the corner 5 mm below and the hole 9 mm above; the probe takes the nearest node's extrapolated stress; syy_inner: as for the outer face; fillet_7: the coarsest mesh, within 5% of the 4 mm mesh; fillet_5: converging: within 2% of the 4 mm mesh
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- **[patch-hex20](../tests/oracle/patch-hex20/)** (theory): Constant-stress patch test, hex20. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
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- **[patch-hex20-reduced](../tests/oracle/patch-hex20-reduced/)** (theory): Constant-stress patch test, hex20-reduced. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
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- **[patch-hex8](../tests/oracle/patch-hex8/)** (theory): Constant-stress patch test, hex8. Source: Irons and Razzaque, 'Experience with the patch test for convergence of finite elements', in Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, pp. 557–587; MacNeal and Harder, Finite Elements in Analysis and Design 1 (1985) 3–20, constant-stress loading, p. 14 Table 7. Tolerances — ux: a patch test is passed exactly: the tolerance only admits rounding; uy: a patch test is passed exactly: the tolerance only admits rounding; uz: a patch test is passed exactly: the tolerance only admits rounding; sxx: a patch test is passed exactly: the tolerance only admits rounding; syy: a patch test is passed exactly: the tolerance only admits rounding; szz: a patch test is passed exactly: the tolerance only admits rounding; sxy: a patch test is passed exactly: the tolerance only admits rounding (stresses of order 1)
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@@ -0,0 +1,21 @@
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# Filleted L-bracket on the octree all-hex mesh
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The corpus part `filleted-bracket` (an 8 mm thick L, 60 × 50 × 40 mm, an R6 fillet inside the
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corner and a Ø8 hole through each leg), built with SolidCraft from `design.json` and meshed by
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`mesh.hex.octree` (hex8 with incompatible modes, steel E = 210 GPa, ν = 0.3). The bottom face of
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the horizontal leg (`F2:side:l1`) is clamped and the top face of the upright leg (`F2:side:l5`)
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carries 2 kN along +x.
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Checked on the 5 mm mesh: equilibrium; the certified validity of every element; the mesh volume
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against the CAD volume; the bending stress of the upright leg at y = 19 on both faces,
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σ_yy = M c / I = 2000 · 31 · 4 / 1706.7 = 145.3 MPa (M is exact by statics, the plane-section
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stress is the reference, the corner and a hole are near). The von Mises stress at the middle of
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the fillet, which has no closed form, is checked for convergence against the 4 mm mesh:
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| mesh size | hexahedra | fillet von Mises (MPa) | σ_yy outer / inner at y = 19 (MPa) |
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|---|---|---|---|
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| 7 mm | 4291 | 138.5 | 149.4 / −146.9 |
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| 5 mm | 13273 | 144.5 | 149.3 / −147.3 |
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| 4 mm (reference) | 21508 | 143.2 | 147.4 / −145.5 |
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A 3 mm mesh needs more than the direct solver's factor cap.
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@@ -0,0 +1,89 @@
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{
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||||
"commands": [
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{
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||||
"command": "sketch.create",
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"params": {
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"plane": "XY",
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||||
"name": "Profile"
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||||
}
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||||
},
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||||
{
|
||||
"command": "sketch.line",
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||||
"params": {
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||||
"points": [
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||||
[
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0,
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0
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],
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[
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60,
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0
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],
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[
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60,
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8
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],
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[
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8,
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8
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||||
],
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||||
[
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8,
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50
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],
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||||
[
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0,
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50
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||||
]
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||||
],
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||||
"closed": true
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}
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||||
},
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||||
{
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||||
"command": "sketch.finish",
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||||
"params": {}
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||||
},
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||||
{
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||||
"command": "solid.extrude",
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||||
"params": {
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"distance": 40,
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"body_name": "Bracket"
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}
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},
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{
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"command": "solid.fillet",
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"params": {
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"edges": [
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[
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8,
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8,
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20
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]
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],
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"radius": 6
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}
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},
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{
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"command": "solid.hole",
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"params": {
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"position": [
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40,
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8,
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20
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||||
],
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"diameter": 8
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||||
}
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},
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||||
{
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||||
"command": "solid.hole",
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"params": {
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||||
"position": [
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8,
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||||
32,
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||||
20
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],
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"diameter": 8
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}
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}
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]
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}
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@@ -0,0 +1,99 @@
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{
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"title": "Filleted L-bracket on the octree all-hex mesh: equilibrium, beam bending, fillet stress convergence",
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"kind": "theory",
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"source": "equilibrium; Euler–Bernoulli bending of the 8 × 40 mm leg, σ = M c / I with M = F (50 − y) (S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed., 1970, §102); grid convergence of the fillet stress against the 4 mm mesh of this case (P. J. Roache, Verification and Validation in Computational Science and Engineering, 1998, ch. 5)",
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"slow": true,
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"quantities": [
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{
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"id": "reaction_x",
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"quantity": "x reaction on the clamped face (5 mm mesh)",
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"measure": {
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"from": "solve5",
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"pointer": "/reaction_total/0"
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},
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"value": -2000.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "the reactions balance the 2 kN load to solver precision"
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},
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{
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"id": "invalid",
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"quantity": "elements the certified Jacobian check does not prove valid (5 mm mesh)",
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"measure": {
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"from": "quality5",
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"pointer": "/invalid/count"
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||||
},
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"value": 0.0,
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"tolerance": {
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"exact": true
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},
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"reason": "the octree mesher returns only elements proven valid"
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},
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{
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"id": "volume",
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"quantity": "mesh volume against the CAD volume (5 mm mesh)",
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"measure": {
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"from": "mesh5",
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"pointer": "/bodies/0/volume"
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},
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"value": 32144.778925,
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"tolerance": {
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"relative": 0.003
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},
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"reason": "bilinear boundary faces on the R6 fillet and the two Ø8 holes, and the 1e-3 chordal tessellation they are fitted to"
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},
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{
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"id": "syy_outer",
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"quantity": "σ_yy on the outer face of the upright leg at y = 19, z = 6 (5 mm mesh)",
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"measure": {
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"from": "probe5",
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"pointer": "/nodes/1/stress/1"
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},
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"value": 145.3125,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "beam theory ignores the corner 5 mm below and the hole 9 mm above; the probe takes the nearest node's extrapolated stress"
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},
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{
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"id": "syy_inner",
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"quantity": "σ_yy on the inner face of the upright leg at y = 19, z = 6 (5 mm mesh)",
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||||
"measure": {
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||||
"from": "probe5",
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||||
"pointer": "/nodes/2/stress/1"
|
||||
},
|
||||
"value": -145.3125,
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||||
"tolerance": {
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||||
"relative": 0.05
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||||
},
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||||
"reason": "as for the outer face"
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||||
},
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||||
{
|
||||
"id": "fillet_7",
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"quantity": "von Mises stress at the middle of the fillet, 7 mm mesh",
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||||
"measure": {
|
||||
"from": "probe7",
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||||
"pointer": "/nodes/0/von_mises"
|
||||
},
|
||||
"value": 143.21,
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||||
"tolerance": {
|
||||
"relative": 0.05
|
||||
},
|
||||
"reason": "the coarsest mesh, within 5% of the 4 mm mesh"
|
||||
},
|
||||
{
|
||||
"id": "fillet_5",
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||||
"quantity": "von Mises stress at the middle of the fillet, 5 mm mesh",
|
||||
"measure": {
|
||||
"from": "probe5",
|
||||
"pointer": "/nodes/0/von_mises"
|
||||
},
|
||||
"value": 143.21,
|
||||
"tolerance": {
|
||||
"relative": 0.02
|
||||
},
|
||||
"reason": "converging: within 2% of the 4 mm mesh"
|
||||
}
|
||||
]
|
||||
}
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||||
@@ -0,0 +1,33 @@
|
||||
{
|
||||
"note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
|
||||
"values": {
|
||||
"fillet_5": {
|
||||
"band": 1.4452906175564113e-7,
|
||||
"value": 144.52906175564112
|
||||
},
|
||||
"fillet_7": {
|
||||
"band": 1.4321000000000002e-7,
|
||||
"value": 138.5286423070889
|
||||
},
|
||||
"invalid": {
|
||||
"band": 0.0,
|
||||
"value": 0.0
|
||||
},
|
||||
"reaction_x": {
|
||||
"band": 2.0000000000000003e-6,
|
||||
"value": -1999.999999998785
|
||||
},
|
||||
"syy_inner": {
|
||||
"band": 1.472793063397077e-7,
|
||||
"value": -147.2793063397077
|
||||
},
|
||||
"syy_outer": {
|
||||
"band": 1.4926027331710374e-7,
|
||||
"value": 149.26027331710372
|
||||
},
|
||||
"volume": {
|
||||
"band": 0.00003217691091849411,
|
||||
"value": 32176.910918494108
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,228 @@
|
||||
[
|
||||
{
|
||||
"command": "model.material.create",
|
||||
"params": {
|
||||
"name": "Steel",
|
||||
"elastic": {
|
||||
"type": "isotropic",
|
||||
"young": 210000.0,
|
||||
"poisson": 0.3
|
||||
}
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "mesh.hex.octree",
|
||||
"params": {
|
||||
"body": "Bracket",
|
||||
"size": 7.0
|
||||
},
|
||||
"id": "mesh7"
|
||||
},
|
||||
{
|
||||
"command": "model.set.create",
|
||||
"params": {
|
||||
"name": "all",
|
||||
"geometry": [
|
||||
{
|
||||
"body": "Bracket"
|
||||
}
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.set.create",
|
||||
"params": {
|
||||
"name": "base",
|
||||
"geometry": [
|
||||
{
|
||||
"body": "Bracket",
|
||||
"face": "F2:side:l1"
|
||||
}
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.set.create",
|
||||
"params": {
|
||||
"name": "top",
|
||||
"geometry": [
|
||||
{
|
||||
"body": "Bracket",
|
||||
"face": "F2:side:l5"
|
||||
}
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.section.create",
|
||||
"params": {
|
||||
"name": "solid",
|
||||
"set": "all",
|
||||
"material": "Steel",
|
||||
"kind": {
|
||||
"type": "solid"
|
||||
},
|
||||
"formulation": {
|
||||
"incompatible_modes": true
|
||||
}
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.boundary_condition.create",
|
||||
"params": {
|
||||
"name": "clamp",
|
||||
"type": "fixed",
|
||||
"target": {
|
||||
"set": "base"
|
||||
}
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.load.create",
|
||||
"params": {
|
||||
"name": "F",
|
||||
"type": "force",
|
||||
"target": {
|
||||
"set": "top"
|
||||
},
|
||||
"vector": [
|
||||
2000.0,
|
||||
0,
|
||||
0
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "model.step.create",
|
||||
"params": {
|
||||
"name": "Load",
|
||||
"procedure": {
|
||||
"type": "static"
|
||||
},
|
||||
"boundary_conditions": [
|
||||
"clamp"
|
||||
],
|
||||
"loads": [
|
||||
"F"
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "mesh.quality",
|
||||
"params": {},
|
||||
"id": "quality7"
|
||||
},
|
||||
{
|
||||
"command": "solve.static",
|
||||
"params": {},
|
||||
"id": "solve7"
|
||||
},
|
||||
{
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Load",
|
||||
"at": [
|
||||
[
|
||||
9.757359312880714,
|
||||
9.757359312880714,
|
||||
10.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
19.0,
|
||||
6.0
|
||||
],
|
||||
[
|
||||
8.0,
|
||||
19.0,
|
||||
6.0
|
||||
]
|
||||
]
|
||||
},
|
||||
"id": "probe7"
|
||||
},
|
||||
{
|
||||
"command": "mesh.hex.octree",
|
||||
"params": {
|
||||
"body": "Bracket",
|
||||
"size": 5.0
|
||||
},
|
||||
"id": "mesh5"
|
||||
},
|
||||
{
|
||||
"command": "mesh.quality",
|
||||
"params": {},
|
||||
"id": "quality5"
|
||||
},
|
||||
{
|
||||
"command": "solve.static",
|
||||
"params": {},
|
||||
"id": "solve5"
|
||||
},
|
||||
{
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Load",
|
||||
"at": [
|
||||
[
|
||||
9.757359312880714,
|
||||
9.757359312880714,
|
||||
10.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
19.0,
|
||||
6.0
|
||||
],
|
||||
[
|
||||
8.0,
|
||||
19.0,
|
||||
6.0
|
||||
]
|
||||
]
|
||||
},
|
||||
"id": "probe5"
|
||||
},
|
||||
{
|
||||
"command": "mesh.hex.octree",
|
||||
"params": {
|
||||
"body": "Bracket",
|
||||
"size": 4.0
|
||||
},
|
||||
"id": "mesh4"
|
||||
},
|
||||
{
|
||||
"command": "mesh.quality",
|
||||
"params": {},
|
||||
"id": "quality4"
|
||||
},
|
||||
{
|
||||
"command": "solve.static",
|
||||
"params": {},
|
||||
"id": "solve4"
|
||||
},
|
||||
{
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Load",
|
||||
"at": [
|
||||
[
|
||||
9.757359312880714,
|
||||
9.757359312880714,
|
||||
10.0
|
||||
],
|
||||
[
|
||||
0.0,
|
||||
19.0,
|
||||
6.0
|
||||
],
|
||||
[
|
||||
8.0,
|
||||
19.0,
|
||||
6.0
|
||||
]
|
||||
]
|
||||
},
|
||||
"id": "probe4"
|
||||
}
|
||||
]
|
||||
Reference in new issue
Block a user