# Analysis of tablet compaction. II. Finite element analysis of density distributions in convex tablets

##### Sinka, I.C.; Cunningham, J.C.; Zavaliangos, A.

#### Journal of Pharmaceutical Sciences 93(8): 2040-2053

#### 2004

**ISSN/ISBN: 0022-3549**

PMID: 15236453

DOI: 10.1002/jps.20111

Accession: 011757995

A Drucker-Prager/cap constitutive model, where the elastic and plastic model parameters are expressed as a function of relative density (RD), was presented in a companion article together with experimental calibration procedures. Here, we examine the RD distribution in curved-faced tablets with special reference to the die wall lubrication conditions. The compaction of powders is examined using finite element analysis, which involves the following factors: constitutive behavior of powder, friction between powder and tooling, geometry of die and punches, sequence of punch motions, and initial conditions that result from die fill. The predictions of the model are validated using experimental RD maps. It is shown that different die wall lubrication conditions induce opposite density distribution trends in identical tablets (weight, height, and material). The importance of the internal tablet structure is illustrated with respect to break force, failure mode, and friability: it is demonstrated that for a given average tablet density the break force and failure mode are not unique. Also, tablet regions having lower density locally have higher propensity for damage. The applicability of finite element analysis for optimizations of formulation design, process development, tablet image, and tool design is discussed.