On the Compaction of Granular Matter; Continuum and Discrete Numerical Modelling

Abstract

Granular materials are ubiquitous in nature and industry alike, ranging from assemblies of large rocks to the finest of powders. Nonetheless, compared to fluids and solids, our understanding of granular materials remains limited, because the macroscopic mechanical behaviour of a granular material strongly depends on the interplay between the mechanical properties and shapes of the individual grains. This becomes particularly apparent when creating powder formulations for pharmaceutical tablets, where the combination of various powders makes mechanical properties difficult to predict. In the pharmaceutical industry, this is known as the formulation problem and creates many difficulties when trying to compact a powder mixture into a tablet, leading to tablet defects such as chipping, capping, and lamination. The inherent complexity of granular matter therefore cannot be captured by simplified theoretical models, such as single-curve fitting, and more advanced numerical simulation methods are required. The central aim of this thesis is thus to address the formulation problem with respect to pharmaceutical powder compaction by using both continuum and discrete numerical methods. A novel framework using the finite element method (FEM) in combination with the density-dependent Drucker-Prager Cap (dDPC) model and mixing/demixing rules is presented and demonstrated to be able to predict the compressibility and stress profiles of a wide range of powder formulations beyond the training data set. This not only allows identification of formulations with a high risk of tablet failure but also suggests that pressurised granular materials posses a representative volume element (RVE) with limited non-local influences. Furthermore, a new technique called the volume-interacting level-set discrete element method (VLS-DEM) is proposed to simulate arbitrarily shaped particles at a reduced computational cost compared to e.g. clumps of spheres when compared at a similar spatial resolution. VLS-DEM thereby allows the use of realistic particles shapes, e.g. obtained from X-ray tomography, including effects caused by angularity, concavity, and interlocking. Together, these methods provide a useful set of novel techniques for the pharmaceutical and granular matter communities to accelerate early-stage formulation development by making predictions of candidate formulations as well as to study the fundamentals of granular materials with respect to particle shape.