Executive Summary
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 (i.e., the MDR 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 manyparticle 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 to extend the contact model to the many-interacting particle case were started, as this was a necessary step to allow simulation of full-scale industrial applications. An initial implementation into LIGGGHTS was carried out and preliminary simulations showed promise in replicating compaction simulator data. Although progress was made, there were problems that remained both from a modeling and computational perspective when attempting to extend to the the many-interacting particles case. On the modeling side, the rigid-flat placement scheme used to extend the MDR contact model formulation to the many-interacting particle case was realized to be inaccurate with increasing polydispersity. On the computational side, a switch from LIGGGHTS to LAMMPS was desirable for three primary reasons: (i) LAMMPS is and will remain fully open-source with continual upkeep from Sandia National Laboratories (SNL), (ii) Joel Clemmer and Dan Bolintineanu, two SNL research scientists and primary contributors to LAMMPS, volunteered to assist with the implementation of the MDR contact model into LAMMPS, and (iii) LAMMPS provides the advantage of allowing immediate coupling with a multi-particle collision dynamics fluid solver, capable of simulating a compressible gas phase.
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In the third year, a fully-parallelized implementation of the many-interacting MDR contact model was integrated into LAMMPS. The implementation was tested using both simple configurations involving a small number of particles and large-scale tableting simulations with tens of thousands of particles. This rigorous testing process prompted an overhaul of the rigid flat placement scheme and the development of a new topological algorithm to prevent contact through material during large deformation DEM. The unique ability of the MDR contact model to reconstruct deformed particle shapes was validated by comparisons with FEM predictions. The industrially relevant problem of pharmaceutical tableting was simulated, with experimental data provided by Vertex Pharmaceuticals for the compaction of Avicel PH102 (microcrystalline cellulose) serving as a benchmark. Good agreement was observed between experiments and numerical simulations for axial and radial stress measurements as functions of axial strain. Notably, the simulation also accurately predicted residual radial stresses after the release of axial confining pressure and the ejection force, aligning with experimental results. Preliminary coupled simulations involving the new DEM implementation and a compressible gas phase were also conducted. These simulations demonstrated that fracture caused by entrapped air could occur under specific loading conditions, though these were outside typical operating ranges.
In summary, a robust and reliable powder DEM model has been developed, which is opensource and accessible to all IFPRI members and is currently being used by some such as Amir Esteghamatian from Merck. Its utility in understanding defect formation in pharmaceutical tableting has been qualitatively demonstrated, and we are now positioned to conduct a comprehensive numerical investigation into air-induced defects. The mechanically-derived nature of the contact model o↵ers two significant advantages: (i) it provides a solid foundation for the future development of a continuum constitutive relation, and (ii) it enables the simulation of a wide range of industrial powder compaction problems beyond tableting, provided the material properties are known.
The following report is split into four chapters. Chapter 1 gives a high level update of the project and details on progress made that is not included in the attached papers. Chapter 2 is the soon to be submitted to Powder Technology paper covering the major advances and results from extending the MDR contact model to the many-interacting particle case. Chapter 3 and 4 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.