Multi-component mixing and demixing model for predictive finite element modelling of pharmaceutical powder compaction

A set of numerical methods is described that allows predictive finite element method (FEM) simulations of the compaction of multi-component pharmaceutical powder formulations across the entire range of compositions. An automated parametrisation procedure was used to extract density-dependent Drucker-Prager Cap (dDPC) model parameters from experimental data. Subsequently, these parameters were interpolated (mixed) or extrapolated (demixed) to predict dDPC model parameters of unseen powder formulations.

Pure, binary, and ternary formulations of micro-crystalline cellulose (MCC, plastic), dibasic calcium phosphate dihydrate (DCPD, brittle), and pre-gelatinised starch (STA, elastic) powders were used to validate the parametrisation and mixing/demixing methodologies. FEM simulations were capable of reproducing compaction curves with errors only marginally greater than the experimental variability. Using only pure component data, FEM simulations with mixing rules were capable of predicting the compaction curves of mixtures as well as their shear stress distributions.

Moreover, with data of only two or three powder formulations, a new demixing methodology was able to predict the behaviour of the constituent powders. The combination of these methodologies provides a powerful tool to rapidly explore powder formulations anywhere within the composition phase diagram, providing compaction curves but also stress profiles that are essential to early-stage formulation process development and tooling design.

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The powders used in this study are micro-crystalline cellulose (MCC, Avicel PH200), dibasic calcium phosphate dihydrate (DCPD, Emcompress premium), and partially pregelatinized starch (Starch, SEPISTAB ST 200). The median particle diameters by volume, or Dv50 values, were 199, 212, and 192 lm, respectively. Aside from the 3 pure powders, this study considers 5 binary and 4 ternary mixtures, giving a total of 12 powder formulations.

Data acquisition

All powder compaction experiments used the MEDELPHARM STYL’One Evolution press (MEDELPHARM, Beynost, France). The press was equipped with an external lubrication device (MEDELPHARM lubrication pack), a 80 kN load cell, circular flat-faced punches (11.28 mm), and an instrumented die. Punch deformation was determined and accounted for using the Analis software (MEDELPHARM, Beynost, France). Force sensors were dual-scale piezoelectric with an accuracy of 1 N, and displacement sensors had an accuracy of 1 lm. After external lubrication with magnesium stearate, the powder was filled into the die using a force feeder and compacted using a uniaxial, double-ended compaction, V-shape profile with a 0.2 mm s1 punch speed (compression speed of 0.4 mm s1). Punches were centred around the radial pressure sensor in the die-wall. In the case of uniaxial compaction and axial symmetry on the z axis, the stresses in the tablet can be described using the hydrostatic stress.

Dingeman L.H. van der Havena, Maria Mikoronib, Andrew Megarryc, Ioannis S. Fragkopoulosb,James A. Elliott, Multi-component mixing and demixing model for predictive finiteelement modelling of pharmaceutical powder compaction, June 2024Advanced Powder Technology 35(7), June 202435(7), DOI:10.1016/j.apt.2024.104513

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