Finite element analysis of pharmaceutical tablet compaction using a density dependent material plasticity model Tuhin Sinha a , Rahul Bharadwaj b , Jennifer S. Curtis c , Bruno C. Hancock b , Carl Wassgren a,d, ⁎ a School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA b Pfizer Global Research and Development, Groton, CT 06340, USA c Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA d Department of Industrial and Physical Pharmacy (by courtesy), Purdue University, West Lafayette, IN 47907, USA abstract article info Article history: Received 21 April 2009 Received in revised form 25 January 2010 Accepted 1 April 2010 Keywords: Constitutive model Powder Tablet compaction Finite element method Drucker–Prager Cap Relative density Finite element method (FEM) simulations of pharmaceutical tablet compaction using a Drucker–Prager Cap (DPC) model are presented in which material properties are relative density (solid fraction) dependent. Results from the solid fraction dependent model are compared to those from a constant property model. Predictions from the solid fraction dependent model more closely match experimental measurements of surface hardness, punch force, and material displacement than the constant property model. These results suggest that FEM simulations using the DPC model should account for material property dependence on local solid fraction. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Tablets are the most common type of pharmaceutical dosage form thanks to their physical and chemical stability, accurate dosing, and low cost. A critical step in the manufacture of these dosage forms is the compaction of a loose powder/granule formulation between two punches within a die. Among other qualities, the resulting compact should have nearly uniform properties with sufficient mechanical strength to avoid breakage and attrition. Numerical modeling can be used as an effective tool for predicting compaction dynamics and the resulting tablet properties. Current empirical methods for predicting compact properties, such as Heckel analysis and Hiestand indices, have some merit, but these methods cannot quantitatively predict the distribution of material properties during different stages of tabletting. A more promising approach is to simulate the powder/compact state using finite element methods (FEMs) in which the powder is treated as a continuous material and the corresponding phenomenological constitutive relations are applied. Such FEM simulations can be used to investigate the influence of tooling geometry, punch force and compaction sequence, and formulation properties so that tablet design may be optimized. 2. Background The continuum approach to modeling powder compaction has been adopted from soil mechanics where phenomenological models have been developed based on experimental characterization. Critical state models determine pressure dependent yield loci that govern the yield state and plastic flow of particulate materials upon com- paction. These models have been successfully adopted in powder metallurgy and ceramics over the last 15 years, yet their application to pharmaceutical powders has been very recent. A variety of continuum models from the soil mechanics literature have been developed from experiments on different geo-materials as described by Schofield and Wroth [24], Di Maggio and Sandler [9], Gurson [13], Green [12], and Drucker et al. [10]. Most of these models are governed primarily by elliptical caps that determine the densification yield loci during the compaction process. However, elliptical caps fail to capture the shearing phenomenon in powders which is extremely important during the decompression and the ejection phases of powder compaction. Only the Drucker–Prager Cap (DPC) model is able to capture these phenomena because of the presence of a shear yield surface in addition to an elliptical cap. Hence, the DPC model has gained wide acceptance as a good constitutive model for modeling powder compaction. The DPC model has been successfully implemented in finite ele- ment methods to predict the evolution of the local mechanical properties during the consolidation of different types of pharmaceutical Powder Technology 202 (2010) 46–54 ⁎ Corresponding author. School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA. E-mail address: wassgren@purdue.edu (C. Wassgren). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.04.001 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec