Concept

Relative density

The fraction of space a lattice fills — and the single strongest predictor of its stiffness.

ρ / ρₛ (log)E / Eₛ (log)stretch n≈1bending n≈2
What it is

Volume fraction sets the scale.

Relative density (or volume fraction) is the share of the unit cell occupied by solid material, from 0 (empty) to 1 (fully dense). It is the first number to fix about any lattice, because effective stiffness follows it closely — as a power law, E/Eₛ ≈ (ρ/ρₛ)ⁿ, where Eₛ and ρₛ are the parent material's modulus and density.

The exponent n measures how efficiently the architecture carries load. Stretch-dominated lattices, whose members are loaded mostly in tension and compression, approach n ≈ 1 — stiffness falls about in proportion to density. Bending-dominated lattices approach n ≈ 2, losing stiffness much faster as they get lighter.

In the tools

One control, every tool.

Each design tool exposes relative density through a thickness control — offset or wall thickness in tpms and wave, half-width in grain and noise, strut radius in beam. The homogenization readout reports the resulting stiffness, so you tune density to a target.

Rule of thumb

Pick the exponent, then the density.

For stiffness per unit weight, prefer a stretch-dominated architecture (low n) and set density as low as the loads allow. For energy absorption or a soft response, a bending-dominated architecture at the same density is the better tool.

See also

Related pages.