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.