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

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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 (X1), kneading time (X2), lubricant-mixing time (X3), and compression force (X4) were selected as design variables. The Drucker–Prager 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 X4. Moreover, an interaction between X2 and X3 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.

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