Finite Element Analysis and Modeling in Pharmaceutical Tableting

Abstract

Finite element analysis (FEA) is a computational method providing numerical solutions and mathematical modeling of complex physical phenomena that evolve during compression tableting of pharmaceutical powders. Since the early 2000s, FEA has been utilized together with various constitutive material models in a quest for a deeper understanding and unraveling of the complex mechanisms that govern powder compression. The objective of the present review paper is to highlight the potential and feasibility of FEA for implementation in pharmaceutical tableting in order to elucidate important aspects of the process, namely: stress and density distributions, temperature evolution, effect of punch shape on tablet formation, effect of friction, and failure of the tablet under stress. The constitutive models and theoretical background governing the above aspects of tablet compression and tablet fracture under diametral loading are also presented. In the last sections, applications of FEA in pharmaceutical tableting are demonstrated by many examples that prove its utilization and point out further potential applications.

Keywords: Drucker–Prager; compression; constitutive models; density distribution; microcrystalline cellulose; overview; pharmaceuticals; punch shape; simulation; tablet shape.

Figure 1

Symmetric geometric 2D model (a) for powder compression and (b) for diametral loading test of tablet mechanical strength.

Figure 2

Flowchart for the application, verification, and validation of a finite element analysis (FEA) model.

Figure 3

(a) The Drucker–Prager Cap (DPC) model and its parameters and (b) family of DPC models for different levels of relative density over a range of compaction.

Figure 4

Elastic stress field developed in a flat-faced tablet during diametrical compression.

Figure 5

Comparison of flat- and optimal convex-faced tablets: (a) relative density (RD) distribution, (b) shear stress distribution within the tablets as they eject from the die, and (c) plot of radial pressure vs. compaction pressure (Adapted with permission from Ref. [96]).

Figure 6

Microcomputed tomopraphy relative density cross-sections (left column) and correlating simulation cross-sections (right column) of a convex tablet (color contour scales represent relative density values). Reprinted with permission from Ref. [106].

Figure 7

3D model of circular tablet under compression showing positive and negative tensile stress in the x direction. Reprinted with permission from Ref. [65].

Figure 8

x-axial stress distribution in elastic tablets with breaking (“score”) line (Adapted with permission from Ref. [90]).