Numerical approach using DEM to control the mechanical strength of pharmaceutical tablets

The present contribution deals with a discrete Element Method (DEM) based on a hybrid particulate lattice model to predict the mechanical strength of pharmaceutical tablets. We consider the classical approach based on the Stress Concentration Force (SCF) obtained at a defect of controlled size. The paper aims at studying the benefits of such a concepts to provide suitable mechanical strength through diamteral compression tests of a cylindrical tablets with a hole. Results exhibited that ratio of 3 between hole and tablet radii is required to obtained proper mechanical strength.


Powders are the most common used materials in the planet that many industries such as food, cosmetics and drug deal with handling and processing them. However, some problems related to the physical and mechanical properties of powder or process parameters can arise during the process leading to nonconformity of the tablets. The most important problems in the pharmaceutical industry are: copping of tablets, adherence or sticking of powder to the wall, low mechanical resistance or bad dissolution of tablets. controlling the behavior of powders during the manufacturing process is of crucial challenges for industries and researchers alike. The complexity of the powder interactions stills a barrier to obtain relevant models adapted to the different processes and situations.

Empirical solutions are often used. Nevertheless, the precision and reproducibility of powder processes are crucial. Understanding the link between powder properties and mechanical strength of tablets is a major step forward in establishing criteria for optimizing the compression and processing properties. The classical approach used in pharmaceutical fields is based on the Stress Concentration Force (SCF) obtained at a defect of controlled size. Mechanical strength of such material depends on its capability to relieve stress concentration. The diametral compression of tablets with a cylindrical hole test is often used.

This approach was introduced in the pharmaceutical field by Hiestand et al. [1]. Review of pharmaceutical literature shows that there is no consensus on the influence of the ratio between the radius of the hole and the radius of the tablet on its mechanical strength [2, 3]. This gives rise to contradictory results concerning the SCF value [4, 5]. Furthermore, we consider that tablets are subjected to relatively homogeneous stresses which is not true. However, tablets are characterized by structural defaults and porous state. To overcome the limits of the exsting modeling, we aim to develop a numerical methodology based on the Discrete Element Method (DEM) to optimize the compression process and control the mechanical performances of pharmaceutical tablets. The DEM is a promising tool to model compression process, from powder bed to the characterization of mechanical properties.

Such an approach has been applied to simulate mechanical behavior of cohesive granular media [6]. Besides, Moukadiri et al. [7] developed a DEM-based approach called halo to study the level of dispersion of the stress obtained at the scale of the particle which is always heterogeneous, even if it is theoretically homogeneous. Leclerc et al. [8] show the suitability of the DEM to simulate cracks initiation and propagation in cohesive granular media. Following the present introduction, the paper is outlined as follows. Section 2 describes the hybrid lattice-particle model used to simulate a cohesive granular medium and the halo approach to determine the level of stress dispersion. In section 3, diametral compression test of pharmaceutical tablet is carried out. Results are in agreement with theoretical solutions in terms of stress fields. In section 4, the influence of ratio between hole and tablet radii on the mechanical strength is investigated. A Special care is taken to accurate control the dispersity of stress fields.

Excipients used in the study besides other: Duralac H from Meggle

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Hamza Haddad, Willy Leclerc, Mohamed Guessasma. Numerical approach using DEM to control the
mechanical strength of pharmaceutical tablets. 15ème colloque national en calcul des structures, Université Polytechnique Hauts-de-France [UPHF], May 2022, 83400 Hyères-les-Palmiers, France.

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