We have carried out simulations of the compaction of model granular beds constructed from Lennard-Jones (LJ) particles using nonequilibrium molecular dynamics (MD). The systems simulated comprised a model die containing either a single granule or many granules that were compacted uniaxially by a vertically moving top wall. The simulations while atomistic in nature can also be considered to have a mesoscopic significance in that the primary LJ particles represent coarse-grained units that comprise a realistically sized macroscopic granule. This representation enables plastic deformation of the individual granules as well as fusion between granules to be modeled at a fundamental level. As a granule is compressed, the constituent particles move past each other, giving rise to its deformation. In a multigranular system, at the points of contact between granules, the surface particles on adjacent granules interact with each other and reproduce many of the features of intergranular bonding observed in real systems. The proposed model, although simple, captures the essential physics of the compaction process in a transparent way. It is able to encompass the transition from mainly elastic to plastic deformation, which is instrumental in affecting the quality of real tablets. Using the developed model, we have explored the effects of compression rate on the deformation behavior of the powder column, the microstructure, and the integrity of the formed tablet. The simulations reproduced a number of well-known effects found in tableting. At high compaction speeds and increased extent of final compaction the system manifested a strong elastic response, giving rise to a tendency for the tablets to laminate on decompaction. Slower compaction speeds allowed more time for greater internal rearrangement or plastic deformation and produced a more structurally uniform and stable tablet at the end of the cycle. The simulations also revealed the underlying cause for high-pressure "hot" spots and regions of weak interaction within the tablet where failure can occur. These points or regions invariably corresponded to incoherent interfaces between granule boundaries, and in some instances to interstitial atoms. The mechanical stability of the tablet was found to depend on the effectiveness of the consolidation of the granules, enhanced effectiveness being characterized by more coherent granule boundaries, resulting in a more uniform pressure distribution and stronger granule-granule interactions.