| name | am-lattice-structures |
| description | AM lattice structures — topology types (BCC/FCC/TPMS), relative density, Gibson-Ashby scaling, mechanical properties, heat exchanger lattices, energy absorption, manufacturability constraints. |
| metadata | {"priority":7,"promptSignals":{"phrases":["lattice structure","AM lattice","cellular lattice","TPMS lattice","BCC lattice","lattice infill","lattice topology"],"minScore":3}} |
AM Lattice Structures — Complete Skill
Lattice Classification
Strut-Based Lattices
BCC (Body-Centered Cubic):
Diagonals from corners to center; 8 struts per unit cell
θ = 54.7° from horizontal; good for shear; poor for compressive stiffness
ρ*/ρ_s = 2√3 π (d/l)² [relative density; d = strut diameter; l = unit cell size]
FCC (Face-Centered Cubic):
Face diagonals; 12 struts per unit cell
Better compressive stiffness than BCC alone
ρ*/ρ_s = 6√2 π/2 × (d/l)²
BCC + Z (vertical + diagonal):
Adds 2 vertical struts to BCC; greatly improves axial stiffness
Best for multi-directional loading; common in aerospace
Octet truss:
Maxwell stability criterion: M = s - 3j + 6 = 0 (pin-jointed; stretch-dominated)
s = struts = 24 (per node), j = joints; best stiffness-density ratio
E/E_s = C₁ × (ρ*/ρ_s) [linear scaling; stretch-dominated]
TPMS (Triply Periodic Minimal Surfaces)
Schwartz P (Primitive):
φ(x,y,z) = cos(x) + cos(y) + cos(z) = t [t controls density]
Smooth surface; no sharp nodes; excellent fatigue; excellent for heat transfer
Gyroid:
φ(x,y,z) = sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0
No self-intersection; two interpenetrating channels → excellent for heat exchanger (hot/cold separated)
Diamond TPMS:
sin(x)sin(y)sin(z) + sin(x)cos(y)cos(z) + cos(x)sin(y)cos(z) + cos(x)cos(y)sin(z) = 0
Higher stiffness than gyroid at same density
TPMS advantages:
No stress concentrations at node joints (smooth surface)
Fatigue life 2–5× better than equivalent strut-based lattice
Excellent heat transfer (high surface area density up to 10,000 m²/m³)
Gibson-Ashby Scaling Laws
Bending-dominated (strut lattices, most open-cell):
E/E_s = C₁ × (ρ*/ρ_s)²
σ_yield/σ_s = C₂ × (ρ*/ρ_s)^1.5
C₁ ≈ 0.1–1.0; C₂ ≈ 0.1–0.5 (depends on lattice topology)
Stretch-dominated (octet, TPMS stiff types):
E/E_s = C₁ × (ρ*/ρ_s)
σ_yield/σ_s = C₂ × (ρ*/ρ_s)
Stiffer per unit density than bending-dominated
Energy absorption (plastic collapse):
U_absorbed = σ_plateau × ε_densification × V [J]
σ_plateau = 0.5 × σ_yield(lattice) [approximate; flat for plateau regime]
ε_densification ≈ 1 - 1.4(ρ*/ρ_s)
Manufacturability Constraints
LPBF minimum strut diameter:
d_min ≥ 0.3–0.5 mm (vertical struts); 0.4–0.8 mm (angled struts)
Slender struts (d/l < 0.05): prone to curling and lack-of-fusion during build
Unit cell size:
L_cell = 2–8 mm typical; < 2 mm: features below resolution; > 8 mm: not truly lattice
Angle from horizontal:
Self-supporting: θ ≥ 45°; struts below 45° need care in orientation
TPMS: inherently self-supporting (no overhangs); superior to strut for AM
Powder removal:
Internal lattice channels must be > 2 mm wide for powder evacuation
Provide exit holes; consider loose powder weight (check if structure can hold powder during build)
Surface finish of lattice:
LPBF strut surface: Ra = 15–30 μm (rough); fatigue initiation from surface
TPMS surface: Ra = 10–20 μm (smoother due to gradual curvature)
Heat Exchanger Lattices
Specific surface area:
A_s/V = 4ρ*/ρ_s × (1/d_strut) [strut lattice]
TPMS gyroid: A_s/V ≈ 2000–5000 m²/m³ at 30% density
Heat transfer performance:
Nu = C × Re^n × Pr^0.33 [C, n depend on lattice topology; higher than conventional fins]
Typical: Nu/Nu_plain_channel ≈ 3–8× improvement
Pressure drop:
ΔP = f × (ρ v²/2) × (L/D_hydraulic)
Lattice: high surface area → higher ΔP than empty channel; optimize trade-off
Gyroid heat exchanger:
Two fluid channels totally separated (no mixing); true counter-flow possible
Applications: aircraft oil cooler, automotive intercooler, medical implant bone scaffold
Bone Scaffold Design
Porosity target: 60–80% (mimics trabecular bone)
Pore size: 300–800 μm (optimal for bone ingrowth)
E/E_s target: match cortical bone stiffness (E ≈ 10–20 GPa for cortical; E ≈ 0.1–5 GPa trabecular)
Scaffold stiffness (avoid stress shielding):
E_scaffold < E_bone → stress transferred to bone → bone remodeling
If E_scaffold >> E_bone → stress shield → bone resorption
Ti-6Al-4V gyroid scaffold:
ρ*/ρ_s = 0.3 (30% density); E_s = 114 GPa
E = 0.3 × (E/E_s from scaling) × E_s ≈ 3–8 GPa → matches trabecular bone
Energy Absorption (Crash)
Specific energy absorption (SEA):
SEA = U_absorbed / m = σ_plateau × ε_densification / ρ* [J/kg]
Comparison:
BCC lattice: SEA ≈ 1–10 kJ/kg
Octet: SEA ≈ 5–20 kJ/kg
Hollow sphere foam: SEA ≈ 2–15 kJ/kg
Design for crash: use graded density (gradient lattice) — softer at impact face → progressive crush
Output
Provide: lattice topology (BCC/octet/gyroid/Schwartz P), relative density ρ*/ρ_s, unit cell size [mm], strut diameter [mm] (strut lattice), effective stiffness E [GPa] and strength σ_yield [MPa], energy absorption SEA [kJ/kg] (if crash), specific surface area [m²/m³] (if heat transfer), powder removal strategy, minimum LPBF resolution check, fatigue life comparison to solid (as fraction), and manufacturability assessment (printable angles, channel clearance).
