Tablet Compaction Simulator 2D (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

Heckel Plot Fit

Fitted K (slope)

–

Theory 1/P_y

0.0182

How it works

This is an independent 2D counterpart of the 3D tablet-press engine, not a flattened view of it. Two things are computed separately here:

Grain contact physics — the granule cross-section runs a real soft-sphere (penalty spring–damper) contact simulation: each disc feels gravity, floor/wall/punch normal forces, and pairwise contact forces from its neighbours, integrated with substeps. Grains physically jostle and settle as the punch descends — they are not just algebraically repositioned.
The Heckel equation — the actual governing law of powder densification, the same one real formulators use: ln[1/(1-D)] = K·P + A, K = 1/P_y, A = ln[1/(1-D₀)]. It drives the target bed height and the readouts; the contact simulation supplies the physical motion consistent with that target.

D(P) = 1 − exp[−(K·P + A)]     H(P) = H₀·D₀/D

Run Heckel Sweep ramps P from 0→300 MPa over a few seconds while sampling y = ln[1/(1-D)] against P, then fits a least-squares line through the samples. The fitted slope should land close to the material's true 1/P_y — small deviations come from the density signal lagging the ramp, exactly as a real compaction-simulator trace lags an instantaneous pressure step.

Hardness index — illustrative Ryshkewitch–Duckworth correlation σ ∝ exp(−b·ε), ε = porosity: strength rises steeply as the last pores close.

Real-world relevance: the Heckel plot (ln[1/(1-D)] vs P) is run on every new tablet formulation to choose a compression force that avoids capping/lamination while still meeting hardness targets.

Powder granules Punch / die wall Heckel plot — measured Heckel plot — theory line