Pharmaceutical Manufacturing Handbook: Production and

1140 TABLET COMPRESSION
4. Estimation of the density distributions within a tablet that may infl uence dissolution
or mechanical properties
5. Estimation of the compaction force necessary to obtain tablets having given
properties
6. Taking into account the effect of the tablet material on the stress distribution
on tooling to aid tool design
7. Assessment of the origin of defect or crack formation
8. Optimization of more complex compaction operations such as bilayer and
trilayer tablets or compression - coated tablets
The demonstration of the validity of the continuum - based modelling approach
to tablet compaction requires familiarity with fundamental concepts of applied
mechanics. Under the theory of such a mechanism, powder compaction can be
viewed as a forming event during which large irrecoverable deformation takes place
as the state of the material changes from loose packing to near full density. Moreover,
it is important to defi ne the three components of the elastoplastic constitutive
models which arose from the growing theory of plasticity, that is the deformation
of materials such as powder within a die:
1. Yield criterion , which defi nes the transition of elastic to plastic deformation
2. Plastic fl ow potential , which dictates the relative amounts of each component
of plastic fl ow
3. Evolution of microstructure , which in turn defi nes the resistance to further
deformation
It is also known that the compression process can be described using static and
dynamic models. In the case of static models, time is not considered, although it is
a very important factor in the deformation process. The viscoelastic reactions are
time dependent, especially for the plastic fl ow.
Recently Picker [21] proposed a three - dimensional (3D) model to help explaining
the densifi cation and deformation mechanism experienced by differently deforming
materials during compression. According to the author, a single description of
the processes during tableting is possible, and thus densifi cation and deformation
properties can be clearly distinguished with a single model. This issue has been
investigated over the last years, and a comprehensive approach has been developed
for the analysis of compaction using continuum mechanics principles. This approach
is based on the following components:
1. Equilibrium equations (balance of forces transmitted through the material)
2. Continuity equation (conservation of mass)
3. Geometry of problem
4. Constitutive behavior of powder (stress – strain behavior)
5. Boundary conditions, including loading (e.g., displacement and velocity) and
friction between tooling and powder
6. Initial conditions (e.g., initial relative density of powder)