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Predicting powder compression with simulation that considers particle density distribution

The pharmaceutical industry standard for powder-compressed tablets and pellets is a homogenized final product. At first glance, this seems readily achievable.

The challenge is that the compression process involves very complex granularity with different stressors, the best practice being that rearrangement occurs best under low stresses so that the material compacts maximally. Furthermore, significant lasting deformation, hardening, or breakage can happen under high stresses. Die-wall contact stresses are often hard to estimate from compaction simulator experiments. It usually takes many experiments and accompanying costly pharmaceutical material to arrive at the optimum process.

Computational simulations, therefore, can play a significant role in achieving quality standards by helping R&D teams to understand complex material behavior, predict failure, and optimize processes. Current industry practices Finite Element Analysis (FEA) to model particle compaction. An initial relative density is assumed throughout the field, and the material is modeled with an extended Drucker Prager (EDP) law, where density is a function of plastic volumetric strain. The die and the punches are modeled as rigid bodies. For a given punch movement, stress and relative density distribution from the simulation then are used to determine the quality of compaction. However, it is easy to see that a uniform density distribution is not a realistic assumption. What if we account for the inhomogeneity inherent to the powder filling process? We decided to test this assumption with a multiscale modeling approach.

Example of cylindrical tablet compression using EDP model as practiced in industry (Han et al, Intl Journal of Solids and Structures 45 (2008) 3088-3106).

Particle simulation using Discrete Element Method (DEM) is good for modeling initial stages of compression, in which packing stresses and overlaps are low — modeling these large number of particles and contact interactions is impractical with FEA. DEM captures the discrete nature of the particles, and FEA works best when there are high stresses and significant deformations. So rather than use FEA for the entire compaction sequence, we developed a hybrid model that make best use of both physics models, using Rocky DEM and Ansys Mechanical coupled solution.

Initially we set up a DEM case and filled the compaction die, capturing lower stresses. When overlaps reached about 5 percent of particle damage, we exported the volume fraction data into the FEA solver. DEM and FEA solvers ran serially, both fully integrated into Ansys Workbench.

The team conducted two case examples that compared the hybrid DEM–FEA approach in mixed and segregated particle groups. The DEM run ended when the bed’s average relative density (RD) was 0.76, then was passed to the FEA case, which used an axisymmetric model with quadratic elements.

At the end of the DEM run, the mixture distribution was very different between the two cases, which were both inhomogenous. The segregated case showed a higher RD value at its bottom center, and the mixed case showed higher RD values near the die wall.

Initial condition from DEM RD distribution in bed
Initial condition from DEM RD distribution in bed.

The FEA portion of the experiment studied die-punch displacement, die-wall contact stabiity, equivalent stresses and volumetric plastic strain variations of the two cases. The resuts clearly showed nonhomogenous regions that could lead to tablet breakage as well as surface cracks that might affect tablet quality and dissolution. None of this would be captured in the current industry standard simulation with uniform relative density. Here are the displacement plots for the 2 inhomogenous cases compared with the homogenous case. Interestingly, they all represent the same average initial density.

FEA displacement results.
FEA displacement results.

The team plans to study parameters and conditions that can help fine-tune the DEM–FEA powder-compression model — such as parametric simulation run with 3-D setups, compaction stages, DOEs with material and process variables, other coupling modes, and the need for more more-nuanced experimental data.

Sunil Acharya

Lead Applications Engineer at Ansys, Ph.D.

Sunil Acharya has been practicing simulations in a product development and research role in industry for over 20 years. Sunil holds a Bachelors (Mech. Eng.) from IIT, Bombay and Masters (Biomed. Eng.), Doctorate (Polymer Engineering) from University of Akron. As a Lead Applications Engineer at Ansys Inc. Sunil’s current focus is on advanced material modeling. Sunil is a member of the NAFEMS Manufacturing Process Simulation Working Group.

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