am-lattice-structures

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).