Effect of Process Variables on the Drucker–Prager Cap Model and Residual Stress Distribution of Tablets Estimated by the Finite Element Method

Abstract

A multivariate statistical technique was applied to clarify the causal correlation between variables in the manufacturing process and the residual stress distribution of tablets. Theophylline tablets were prepared according to a Box-Behnken design using the wet granulation method. Water amounts (X 1 ), kneading time (X 2 ), lubricant-mixing time (X 3 ), and compression force (X 4 ) were selected as design variables. The DruckerPrager cap (DPC) model was selected as the method for modeling the mechanical behavior of pharmaceutical powders. Simulation parameters, such as Young's modulus, Poisson rate, internal friction angle, plastic deformation parameters, and initial density of the powder, were measured. Multiple regression analysis demonstrated that the simulation parameters were significantly affected by process variables. The constructed DPC models were fed into the analysis using the finite element method (FEM), and the mechanical behavior of pharmaceutical powders during the tableting process was analyzed using the FEM. The results of this analysis revealed that the residual stress distribution of tablets increased with increasing X 4 . Moreover, an interaction between X 2 and X 3 also had an effect on shear and the x-axial residual stress of tablets. Bayesian network analysis revealed causal relationships between the process variables, simulation parameters, residual stress distribution, and pharmaceutical responses of tablets. These results demonstrated the potential of the FEM as a tool to help improve our understanding of the residual stress of tablets and to optimize process variables, which not only affect tablet characteristics, but also are risks of causing tableting problems.Key words tablet; simulation; mathematical model; residual stress; processing; Bayesian networkVarious stresses, such as shear and axial stress, remain in tablets after the tableting process, because of the induction of elastic recovery. This type of stress, which is termed the residual stress distribution of the tablet, affects tablet characteristics and causes tableting problems. For instance, tablet failure, in particular capping, is more likely to be associated with an intensive shear band formed during the decompression stage.1,2) Therefore, controlling the residual stress distribution of tablets is crucial in pharmaceutical design.However, it is difficult to measure the residual stress distribution of tablets using analytical instruments. For this reason, the finite element method (FEM), in which the powder is modeled using the Drucker-Prager cap (DPC) model, is used to estimate the residual stress distribution of tablets.3,4) The FEM is a numerical analytical method that is well established for the modeling of the deformation of powders in various industries, such as compaction in ceramic industries, and for the analysis of pharmaceutical-powder compaction. 5,6) In the FEM, powders are modeled as continuum media and the compaction behavior is analyzed by solving boundary value problems.The DPC model is one of the continu...

Finite Element Analysis and Modeling in Pharmaceutical Tableting

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