Same physics as the 3D lattice-implant simulator, drawn as three plots an engineer would actually sketch on paper instead of a rendered part. A solid Ti-6Al-4V implant (E ≈ 110 GPa) is roughly 5–6× stiffer than cortical bone (E ≈ 20 GPa); under load the stiffer body carries a disproportionate share of it, and under-stressed bone remodels itself away (Wolff's law) — stress shielding, a real driver of aseptic implant loosening.
Gibson–Ashby scaling: E* / Es = C · (ρ*/ρs)^n
cubic (bending): n = 2, C = 1.00
diamond (mixed): n = 1.5, C = 0.50
octet (stretch): n = 1, C = 0.33
Parallel load-sharing (implant lattice ∥ surrounding bone,
equal axial displacement — a genuine two-spring circuit):
k_implant = E* · A_implant k_bone = E_bone · A_bone
d = F_total / (k_implant + k_bone)
F_implant = k_implant · d F_bone = k_bone · d
- Top-left — 2D unit-cell truss elevation: a real front-on cross-section of the strut lattice (not a flattened 3D camera shot). Strut thickness follows the same relative-density scaling as the 3D version; the whole column compresses live by the actual spring displacement d computed above.
- Bottom — parallel-spring circuit: the implant lattice and the bone tube redrawn as two literal springs sharing one load plate under an equal-displacement constraint. Coil pitch narrows with stiffness; the force arrows are sized by F_implant and F_bone, which always sum to the applied load.
- Top-right — osseointegration curve: suitability score vs. pore size, scored against the ~300–600 µm window where osteoblasts reliably vascularise a printed lattice — the live marker tracks the pore-size slider along the actual Gaussian curve instead of a single number.
Real orthopedic and craniomaxillofacial implants (hip stems, spinal cages, cranial plates) are printed with exactly this kind of graded lattice for precisely this reason: match stiffness to bone, keep pores in the osseointegration window.