The focus of this project is to understand the physical mechanisms that lead to defect formation – pitting, cracking, and delamination – during pharmaceutical tableting. A leading hypothesis among IFPRI members is that trapped interstitial air leads to high pore pressures that tend to fracture adhered particle interfaces after removal of the confining pressure. The project objective is to explore this problem through coupled numerical methods including: i) continuum mixture models and ii) the discrete element method (DEM) coupled with a fluid solver. The primary barrier to using these methods is that fact that the behavior of cohesive powders is not well understood, with neither a generally accepted constitutive relation nor contact model in existence.
To address this, the project has emphasized developing a reliable cohesive powder contact model for usage in DEM. This is the natural progression, since a powder DEM model will be indispensable in determining a constitutive relation for continuum simulations. In particular, we have concentrated on creating a mechanically-derived contact model for adhesive elastic-perfectly plastic particles.
In year one of the project, the majority of the theoretical framework for the contact model was developed, but a number of issues remained. The JKR-type adhesion of the contact model needed to be validated once significant plastic deformation had occurred and the scheme to respect plastic incompressibility required an overhaul. The contact model was limited to simple symmetric loadings of a single particle, necessitating adaptation to many-particle interactions. Additionally, the model, initially coded in Matlab, needed implementation in an established software like LIGGGHTS or LAMMPS, with a reliable fluid-solid coupling strategy.
In year two, the theoretical framework was completed by validating the adhesive model within the fully-plastic regime and correcting the plastic incompressibility scheme. The completed contact model was published in the premier solid mechanics journal, Journal of Mechanics and Physics of Solids, as a two part series. E↵orts have extended to modeling many-particle interactions, a necessary step to allow simulation of full-scale industrial applications. Implementation into LIGGGHTS is underway and preliminary simulations show promise in replicating compaction simulator data. In the upcoming phase, we are working directly with Sandia National Laboratories to create a LAMMPS implementation. In addition to greater computational e ciency and formal support for the model, LAMMPS provides the advantage of allowing immediate coupling with a multi-particle collision dynamics fluid solver, capable of simulating a compressible gas phase.
In summary, the project has made substantial progress on the front of creating a reliable powder DEM model and we are now poised at an exciting place where beginning to understand defect formation during pharmaceutical tableting is tangible. Because the model is mechanically-derived, it can also be trusted to assist in the future development of a continuum constitutive relation. Finally, because of the planned open-source nature of the implementation into LAMMPS, a familiar software to most IFPRI members, the powder DEM model can be used for industrial applications extending beyond tableting.
The following report is split into three chapters. Chapter 1 gives a high level update of the project, without detailed technical explanations and equations. Chapter 2 and 3 are both papers of the two part series published in the Journal of Mechanics and Physics of Solids. These papers contain detailed explanations regarding the theoretical background of the contact model in addition to validations made against finite element simulations. Throughout Chapter 1, references to the two papers are made directing the reader to pertinent information to supplement understanding, however, Chapter 1 was written with the intention that it could be understood without reference to the papers.