1. Introduction
The shear cell is the gold standard bulk solid flowability characterisation test for quasistatic flow regime applications where the consolidating pressures are high and/or the strain rates in the bulk solid are low [1]. Examples include silo and hopper discharge as well as compaction systems like tablet presses.
Shear Cell model files can be downloaded from here:
Additional EDEM Calibration Kits (cone penetrometer, Dynamic and Static Angle of Repose, FT4 Rheometer, Inclined Plane Test, Rotational Shear Cell and Uniaxial compression test files can be found in this post:
Shear cell measurements are commonly used as benchmarks for the calibration of Discrete Element Method (DEM) material models for quasistatic applications[2].
Shear cell testing consists of directly shearing a bulk solid sample under confinement via a rotational or translational motion of a shear lid while applying normal stress to the lid [3], [4].
A computationally efficient approach to modeling the shear cell test using DEM is to reduce it to a periodic cell with a length scale of no less than 20 average particle diameters, as shown in Figure 1[5].
Figure 1: Simulation setup for shear cell test in EDEM (a) unit cell representative of bulk solid, (b) filled nonspherical particles with a normal size distribution, and (c) schematic representation of lid kinematics 
The shear cell test consists of multiple cycles, each comprising of a preshear stage where the material is sheared to a steady state (corresponding to the critical state) and a shear stage where the material is sheared under a reduced load (in the overconsolidated state) as shown in Figure 2. The preshear normal stress remains constant between cycles, but the shear normal stress is progressively reduced. Each cycle yields a point on the shear vs normal stress (στ) plot. The linear fit through those points is termed the yield locus and is the fundamental measurement of the shear cell. An example of a set of yield points and the corresponding yield locus is shown in Figure 3(c) marked a, b, and c.
Figure 2: Exaggerated view (time step 027 s of 73 s simulation) highlighting various stages of cycle 1 in the shear cell simulation. 
Figure 3: Response of the simulation for one shear cell test highlighting the application of (a) shear stress, (b) normal stress, and (c) derived στ plots representing key flow properties 
A yield locus is the yield limit of a bulk solid in the στ dispace and is uniquely defined by four fundamental parameters  the major principal stress, the unconfined yield strength, the effective angle of internal friction, and the angle of internal friction. These parameters are shown in Figure 3 and can be obtained via Mohr circle analysis as follows:
The ratio of major consolidating stress σ1 to unconfined yield strength σc, termed the flow function coefficient, is a common metric for the flowability characterization of bulk solids in the quasistatic flow regime.
2. Modelling methodology
The modeling methodology for the shear cell test follows a unit cell approach similar to the one proposed by Ketterhagen et al. [5]. A representative cubic sample of the bulk solid is generated to a predefined solid fraction using EDEM’s volume packing tool. The sample length scale should be at least twenty times the average particle diameters to avoid artificial jamming effects. The sample is bound by two ribbed plates, as shown in Figure 1(a), where the top plate (named ‘Lid’ in the model) is movable while the bottom plate (named ‘Base’ in the model) is fixed. The 'Lid' is given translational degrees of freedom along the vertical Z and horizontal X global Cartesian directions to apply normal and shear loads to the bulk solid. Linear periodic boundaries are imposed in the X and Y global Cartesian directions to approximate plane strain conditions and enable the large shear deformations required for achieving the critical state.
The bulk solid is modeled using the twosphere particle shape with an aspect ratio of 1.5 shown in Figure 1(b) in order to capture shear dilation in the bulk solid [6]. A normal particle size distribution with a 15 percent coefficient of variance is used to avoid artificial crystallization in the granular assembly[5]. The Edinburgh ElastoPlastic Adhesive (EEPA) model is used to describe the particle contact mechanics. This model can capture the stresshistorydependent behavior that is characteristic of fine particulate solids and commonly quantified by the shear cell yield locus [7].
The loading sequence, described in Figure 3, is imposed on the numerical sample using EDEM’s motion controller feature. The motion controller settings corresponding to the preshear stage are shown in Figures 4 and 5. To achieve a controlled normal stress application a speed cap is enabled for the linear translation of the lid. This capping velocity is typically of the order of five average particle diameters per second. The sample at different stages of loading is shown in Figure 6.
Figure 4: Use of motion controllers to account for particlegeometry forces during normal loading of the specimen 
Figure 5: Use of linear translation for inducing shear in the bulk solid specimen 
Figure 6: Process flow for shear cell test in EDEM where x1 is the force corresponding to pre shear compression stress 
The shear cell measurements are performed in a quasistatic flow regime (strainrate independent) and the shear rate or particle density in the simulation can be increased in the interest of computational efficiency provided that the quasistatic conditions are maintained. In practice this can be achieved by keeping the Inertial number I defined in Equation 1 within the range I<1e3 where the inertial effects are negligible and a strain rate independent behavior consistent with the quasistatic flow regime is observed [8].
(1) 

(2) 
Where is the shear strain rate, d is the particle diameter, P is the hydrostatic pressure, and ρ is the bulk density. The distance between the lid and the base is l, moving at a relative velocity of v, as shown in Figure 1.
Example results for the preshear and shear stages of shear cell tests at varying inertial numbers are shown in Figure 7(a). It can be observed that the results are approximately constant for I < 01e3 but the simulation time reduces linearly with I.
It is also possible to maintain the results at varying geometric scales when using the EEPA model by scaling the pulloff force and surface energy according to Equations 3 to 5 [9]. Note that the ratio of particle diameter to sample length needs to be maintained. Example results for the preshear and shear stages of a shear cell test at varying geometric scales are shown in Figure 7(b) and an excellent agreement can be observed over a wide range of particle diameters.
(3) 

(4) 

(5) 
Where D is the particle diameter, f0 is the EEPA constant pulloff force, γ is the EEPA surface energy, and l is the sample length scale.
Figure 7: Variation of shear stress profile with varying (a) inertial number and (b) particle diameter 
3. Postprocessing with EDEMpy
The shear test results shown in Figure 3 can be automatically exported from the completed EDEM simulations using the ‘Generic_shear_cell_test_analyst.py’ script provided with the example shear cell model here. This Python script utilizes the EDEMpy library for postprocessing EDEM simulation data to compute and export the results in graphs such as the ones shown in Figure 3 and commadelimited files like the one shown in Figure 8a.
This Python script file is accompanied by the settings file ‘Generic_shear_cell_settings.txt’ shown in Figure 8(b) which defines the key time steps for postprocessing of the different test cycles as well as the required outputs.
Figure 8: (a) Extracted responses from the EDEM simulation deck (b) settings file read by the Python postprocessing script 
Multiple simulation decks can be postprocessed by arranging files into one of two configurations, as shown in Figure 9. In configuration two (Figure 9(b)), each simulation deck can be postprocessed with its custom setting file whereas, in configuration one (Figure 9(a)), a single setting file is read for postprocessing of all the EDEM decks. The following sequence outlines the workflow for postprocessing.
Figure 9: Configuration of folders for postprocessing using the ‘Generic_shear_cell_test_analyst.py’ script (a) single setting applicable to all EDEM decks, and (b) provision for custom settings for each simulation deck. 
Only complete simulations with setting files will be postprocessed, otherwise an error message, as shown in Figure 10, will be generated. To avoid file overwriting, all simulation files should have unique folders and simulation names.
Figure 10: Possible error messages that could be encountered during postprocessing 
4. References
[1] D. Schulze, Powders and bulk solids, Schulze: P. SpringerVerlag Berlin Heidelberg, 2008.
[2] C. J. Coetzee, “Review: Calibration of the discrete element method,” Powder Technol., vol. 310, pp. 104–142, 2017, doi: 10.1016/j.powtec.2017.01.015.
[3] ASTM D6773. "Standard shear test method for bulk solids using the Schulze ring shear tester." ASTM International, p. 27, 2002. doi: 10.1520/D677316.
[4] ASTM Standard D612816 "Standard Test Method for Shear Testing of Bulk Solids Using the Jenike Shear Tester."ASTM International, p. 20. doi: 10.1520/D612816.
[5] W. Ketterhagen and C. Wassgren, “A perspective on calibration and application of DEM models for simulation of industrial bulk powder processes,” Powder Technol., vol. 402, p. 117301, 2022, doi: 10.1016/j.powtec.2022.117301.
[6] J. Härtl and J. Y. Ooi, “Numerical investigation of particle shape and particle friction on limiting bulk friction in direct shear tests and comparison with experiments,” Powder Technol., vol. 212, no. 1, pp. 231–239, 2011, doi: 10.1016/j.powtec.2011.05.022.
[7] S. C. Thakur, J. Y. Ooi, and H. Ahmadian, “Scaling of discrete element model parameters for cohesionless and cohesive solid,” Powder Technol., vol. 293, pp. 130–137, 2016, doi: 10.1016/j.powtec.2015.05.051.
[8] G. D. R. Midi, “On dense granular flows,” Eur. Phys. J. E, vol. 14, no. 4, pp. 341–365, 2004, doi: 10.1140/epje/i2003101530.
[9] S. C. Thakur, J. Y. Ooi, and H. Ahmadian, “Scaling of discrete element model parameters for cohesionless and cohesive solid,” Powder Technol., vol. 293, pp. 130–137, 2016, doi: 10.1016/j.powtec.2015.05.051.