Graded-Porosity Lattice Implant & Stress Shielding

Lattice Design

Porosity 55%

Unit-cell topology

Pore / unit-cell size 450 µm

Applied axial load 700 N

Live Readouts

Effective implant modulus— GPa

Bone load share (anti-shielding)— %

Osseointegration suitability—

How it works

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 — the bone next to it is under-stressed, and under-stressed bone remodels itself away (Wolff's law). This is stress shielding, a real driver of aseptic implant loosening. 3D-printed lattice infill lets an implant's effective stiffness be dialled down toward bone's own, while its open pores let bone tissue grow directly into the structure (osseointegration).

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 ∥ surrounding bone,
equal axial displacement):
  bone load share = (Eb·Ab) / (Eb·Ab + E*·Ai)

Porosity sets relative density ρ*/ρs = 1 − porosity. Higher porosity → lower effective modulus E* → more load passes into the bone instead of being shielded by the implant.
Topology changes the deformation mode: bending-dominated cubic struts lose stiffness fast as they thin (n=2); stretch-dominated octet struts stay comparatively stiff at the same porosity (n=1) — the exponents follow Gibson & Ashby's cellular-solids theory and Deshpande–Fleck–Ashby octet-truss analysis.
Pore size is scored against the ~300–600 µm window where osteoblasts reliably vascularise and infiltrate a printed lattice — too small and cells can't get in, too large and the strut network loses coherence.
Applied load converts the bone's load share into an absolute stress reading — it doesn't change the modulus, only how much force is actually flowing at this instant.

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.

Cortical bone tube Lattice strut (color = local load)

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