Tablet Compaction Simulator (Heckel Plot)

Compaction Pressure

Punch pressure P 40 MPa

Material

Mean yield pressure P_y 55 MPa

Initial fill density D₀ 45%

Compact State

Relative density D

45.0%

Porosity ε

55.0%

Bed height

12.0 mm

Hardness index

0.0

How it works

Under uniaxial punch pressure, a powder bed densifies according to the empirical Heckel equation, the standard model used to characterise how pharmaceutical powders compress into tablets:

ln[1 / (1 - D)] = K·P + A
K = 1 / P_y   (P_y = mean yield pressure)
A = ln[1 / (1 - D₀)]

Solving for the relative density D (the fraction of true solid volume occupied, D = ρ_bulk/ρ_true) gives:

D(P) = 1 − exp[−(K·P + A)]

P (punch pressure) — the compaction stress applied by the tablet press punches.
P_y (mean yield pressure) — a material property: how easily the granules deform plastically. A low P_y (e.g. microcrystalline cellulose, ductile) densifies fast with pressure; a high P_y (brittle, fragmenting excipients) needs far more pressure for the same density.
D₀ (initial fill density) — the loose/tapped packing fraction before any pressure is applied, set by particle shape, size distribution and flow.
Because mass and true density are fixed, bed height scales as H = H₀·D₀/D — the punch visibly descends as the bed densifies.
Hardness index is the illustrative Ryshkewitch–Duckworth correlation σ ∝ exp(−b·ε) (ε = porosity) — real tensile strength also depends on bonding area and material, but strength rising steeply as the last pores close is the qualitative behaviour every formulator relies on.

Real-world relevance: this exact D–P relationship (plotted as ln[1/(1−D)] vs P, the "Heckel plot") is run on every new pharmaceutical powder blend to pick a safe compression force — too little and the tablet is friable, too much and capping/lamination or punch wear results.

Powder granules Punch / die wall

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.