Bibliography and Acknowledgements

General DEM

Cundall P.A. and Strack O.D.L. (1979) A discrete numerical model for granular assemblies. Géotechnique, 29(1): p. 47-65.

Goldsmith W. (1960) Impact: The Theory and Physical Behaviour of Colliding Solids. 1st ed. London: Arnold, E.

Ning Z. (1995) Elasto-plastic Impact of Fine Particle and Fragmentation of Small Agglomerates. University of Aston in Birmingham.

Ning Z.  et al. (1997) Effect of particle size and bond strength in impact breakage of weak agglomerates. in Powders & grains 97. Durham, North Carolina.

Ning Z.  et al. (1997) Distinct element simulation of impact breakage of lactose agglomerates. Advanced Powder Technology, 8(1): p. 15-37.

Raji A.O. (1999) Discrete element modelling of the deformation of bulk agricultural particulates. School of Agriculture, Food and Rural Development. Newcastle University.

Zhang D. and Whiten W.J. (1996) The calculation of contact forces between particles using spring and damping models. Powder Technology, 88(1): p. 59-64.

Mio H.  et al. (2009) Speed-up of computing time for numerical analysis of particle charging process by using discrete element method. Chemical Engineering Science, 64(5): p. 1019-1026.

Tsuji Y.  et al. (1992) Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology, 71(3): p. 239-250.

Di Renzo A. and Di Maio F.P. (2004) Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chemical Engineering Science, 59(3): p. 525-541.

Hertz H. (1882) On the contact of elastic solids. Journal fur die Reine und Angewandte Mathematik, 1882(92): p. 156-171.

Mindlin R.D. (1949) Compliance of elastic bodies in contact. Journal of Applied Mechanics, 16: p. 259-268.

Mindlin R.D. and Deresiewicz H. (1953) Elastic Spheres in Contact under Varying Oblique Force. ASME, Journal of Applied Mechanics, 20: p. 327-344.

Sakaguchi H.  et al. (1993) Plugging of the Flow of Granular Materials during the Discharge from a Silo. International Journal of Modern Physics B, 07(09n10): p. 1949-1963.

Contact Models

Hertz-Mindlin Nassuaser-Kuna

Nassauer, B., Kuna, M. Contact forces of polyhedral particles in discrete element method. Granular Matter 15, 349–355 (2013).

Hertz-Mindlin (no slip) with Rvd Rolling Friction

Zhou Y.C.  et al. (1999) Rolling friction in the dynamic simulation of sandpile formation. Physica A: Statistical Mechanics and its Applications, 269(2): p. 536-553.

Ai J.  et al. (2011) Assessment of rolling resistance models in discrete element simulations. Powder Technology, 206(3): p. 269-282.

Hertz-Mindlin with JKR Cohesion

Johnson K.L.  et al. (1971) Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 324(1558).

Baran O.  et al. (2009) DEM Simulation of a Schulze Ring Shear Tester. AIP Conference Proceedings. 1145(1).

Gilabert F.  et al. (2007) Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states. Physical review E, 75(1)

Hertz-Mindlin with JKR Cohesion Version 2

Thornton C. (2015) Granular Dynamics, Contact Mechanics and Particle System Simulations: A DEM Study. Vol. 24. Springer.

Edinburgh Elasto-Plastic Adhesion Model

Jones R. (2003) From Single Particle AFM Studies of Adhesion and Friction to Bulk Flow: Forging the Links. Granular Matter, 4(4): p. 191-204.

Jones R.  et al. (2004) Frictional forces between cohesive powder particles studied by AFM. Ultramicroscopy, 100(1): p. 59-78.

Thakur S.C.  et al. (2014) Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model. Granular Matter, 16(3): p. 383-400.

Capece, M., Ho, R., Strong, J., & Gao, P. (2015). Prediction of powder flow performance using a multi-component granular Bond number. Powder Technology, 286, 561–571.

O'Sullivan, C. and Bray, J., 2004. Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme. Engineering Computations, 21(2/3/4), pp.278-303.

Linear Cohesion V2

Mitarai N. and Nori F. (2006) Wet granular materials. Advances in Physics, 55(1-2): p. 1-45.

Volume Spring

Govender, N., Wilke, D. N., Pizette, P., & Abriak, N. E. (2018). A study of shape non- uniformity and poly-dispersity in hopper discharge of spherical and polyhedral particle systems using the Blaze-DEM GPU code. Applied Mathematics and Computation, 319 , 318336.


Govender, N., Wilke, D. N., Wu, C. Y., Tuzun, U., & Kureck, H. (2019). A numerical investigation into the effect of angular particle shape on blast furnace burden topography and percolation using a GPU solved discrete element model. Chemical Engineering Science, 204 , 926.


Govender, Nicolin, Rajamani, Raj, Wilke, Daniel N, Wu, Chuan-Yu, Khinast, Johannes and Glasser, Benjamin J (2018) Effect of particle shape in grinding mills using a GPU based DEM code. Minerals Engineering, 129. pp. 71-84.


J. Chen, Discrete element method for 3D simulations of mechanical systems of nonspherical granular materials, PhD thesis, The University of Electro-Communications (2012).

Hertz-Mindlin with Bonding

Potyondy D.O. and Cundall P.A. (2004) A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41(8): p. 1329-1364.

Hertz-Mindlin with Archard Wear

Archard J.F. (1953) Contact and Rubbing of Flat Surfaces. Journal of Applied Physics, 24(8): p. 981-988.

Oka Wear

Oka , Y. I., Okamura, K., & Yoshida, T. (2005). Practical estimation of erosion damage caused by solid particle impact: Part 1: Effects of impact parameters on a predictive equation. Wear 259(1–6), 95–101.

Oka, Y. I., & Yoshida, T. (2005). Practical estimation of erosion damage caused by solid particle impact: Part 2: Mechanical properties of materials directly associated with erosion damage. Wear 259 (1–6), 102–109.

Hertz-Mindlin with Heat Conduction

Chaudhuri B.  et al. (2006) Modeling of heat transfer in granular flow in rotating vessels. Chemical Engineering Science, 61(19): p. 6348-6360.

Hysteretic Spring

Walton O.R. and Braun R.L. (1986) Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology, 30(5): p. 949-980.

Walton O.R. and Braun R.L. (1986) Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mechanica, 63(1): p. 73-86.

Walton O.R. (2006)  (Linearized) Elastic-Plastic contact model. DEM Solutions Ltd. Edinburgh, UK.

Type C Rolling Friction

Ai, Jun & Chen, Jian-Fei & Rotter, J. & Ooi, J.. (2011). Assessment of rolling resistance models in discrete element simulations. Powder Technology. 206. 269-282. 10.1016/j.powtec.2010.09.030. 


Casper M.J. (1997) Physical chemistry of surfaces (3rd). Chapter5. Adamson A.W. and Gast A.P., Editors. John Wiley & Sons, Inc.

Hogue M.D.  et al. (2008) Calculating the trajectories of triboelectrically charged particles using Discrete Element Modeling (DEM). Journal of Electrostatics, 66(1): p. 32-38.


Greason W.D. (2000) Investigation of a test methodology for triboelectrification. Journal of Electrostatics, 49(3): p. 245-256.

Tavares UFRJ Breakage Model

King R.P. (2001) 5 - Comminution operations, in Modeling and Simulation of Mineral Processing SystemsKing R.P., Editor. Butterworth-Heinemann: Oxford. p. 127-212.

Tavares L.M. and King R.P. (2002) Modeling of particle fracture by repeated impacts using continuum damage mechanics. Powder Technology  123(2): p. 138-146.

Tavares L.M. (2009) Analysis of particle fracture by repeated stressing as damage accumulation. Powder Technology  190(3): p. 327-339.

Tavares L.M. and de Carvalho R.M. (2012) Modeling ore degradation during handling using continuum damage mechanics. International Journal of Mineral Processing  112-113: p. 1-6.

de Carvalho R.M. and Tavares L.M. (2013) Predicting the effect of operating and design variables on breakage rates using the mechanistic ball mill model. Minerals Engineering  43-44: p. 91-101.

Cavalcanti P.P.  et al. (2019) Surface breakage of fired iron ore pellets by impact. Powder Technology  342: p. 735-743.

Napier-Munn T.J.  et al. (1996) Mineral comminution circuits: their operation and optimisation. JKMRC monograph series in mining and mineral processing. Vol. 2. Indooroopilly, Qld Australia.

Tavares L.M. (2007) Breakage of Single Particles: Quasi-Static, in Handbook of Powder Technology. Elsevier B.V.

Tavares L.M. and das Neves P.B. (2008) Microstructure of quarry rocks and relationships to particle breakage and crushing. International Journal of Mineral Processing  87(1): p. 28-41.

Saeidi F.  et al. (2016) A phenomenological model of single particle breakage as a multi-stage process. Minerals Engineering  98: p. 90-100.

Sun C.T. and Jin Z.H. (2012) Chapter 2 - Griffith Theory of Fracture, in Fracture MechanicsSun C.T. and Jin Z.H., Editors. Academic Press: Boston. p. 11-24.

Tavares L.M. and Chagas S.A. (2020) A stochastic particle replacement strategy for simulating breakage in DEM. Powder Technology (in press) 

King R.P. and Bourgeois F. (1993) Measurement of fracture energy during single-particle fracture. Minerals Engineering  6(4): p. 353-367.

Tavares L.M. and King R.P. (1998) Single-particle fracture under impact loading. International Journal of Mineral Processing  54(1): p. 1-28.

Barrios G.  et al. (2015) DEM Simulation of Bed Particle Compression Using the Particle Replacement Model, in 2nd International Conference on Energy, Sustainability and Climate Change. Crete, Greece.

Bond F.C. (1946) Crushing Tests by Pressure and Impact. Mining Technology  169: p. 58-65.

Particle Body Forces

Temperature Update

Chaudhuri B.  et al. (2006) Modeling of heat transfer in granular flow in rotating vessels. Chemical Engineering Science, 61(19): p. 6348-6360.

Lift and Drag Models

Norouzi H. et al. (2016) Coupled CFD-DEM modelling, formulation, implementation and application to multiphase flows (1st). Chapter6. John Wiley & Sons, Inc.

Sommerfeld M and Laín S. (2012) Numerical calculation of pneumatic conveying in horizontal channels and pipes : Detailed analysis of conveying behaviour. International Journal of Multiphase Flow, 39: p. 105-120.

Morsi S. A. J and Alexander A. J. (1972) An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics, 55(2): p. 193-208.

Schiller L and Naumann A. (1933) A drag coefficient correlation. Vdi Zeitung,  77: p. 318-320

Chhabra R. P. et al. (1999) Drag on non-spherical particles: an evaluation of available methods. Powder Technology, 101(3): p. 288-295.

Powder Starter Pack

Carr R.L. (1965) Evaluating Flow Properties of Solids. Chemical Engineering Journal, 72(69)

Wells J.I. (1988) Pharmaceutical preformulation. Physicochemical Properties of Drug Substances, ed. Rubinstein M.M.E. Chichester: Ellis Horwood Limited. 209-214.

Marshall K. (1986) Compression and Consolidation of Powdered Solids, The Theory and Practise of Industrial Pharmacy(3rd). Lieberman H., Lachman, L., Editor. Lea & Febiger.

World Health Organization (WHO). (2017) Bulk Density and Tapped Density Of Powders, The International Pharmacopoeia (4th).

Guerin E.  et al. (1999) Rheological characterization of pharmaceutical powders using tap testing, shear cell and mercury porosimeter. International Journal of Pharmaceutics, 189(1): p. 91-103.

Powders Database

ASTM D6393 / D6393M-21, Standard Test Method for Bulk Solids Characterization by Carr Indices, ASTM International, West Conshohocken, PA, 2021,

ASTM D6128-16, Standard Test Method for Shear Testing of Bulk Solids Using the Jenike Shear Tester, ASTM International, West Conshohocken, PA, 2016, 

ASTM D6773-16, Standard Test Method for Bulk Solids Using Schulze Ring Shear Tester, ASTM International, West Conshohocken, PA, 2016,

Härtl, J., & Ooi, J. Y. (2011). Numerical investigation of particle shape and particle friction on limiting bulk friction in direct shear tests and comparison with experiments. Powder Technology, 212(1), 231–239.

EDEM 2021.2 Documentation

Thakur, S. C., Ooi, J. Y., & Ahmadian, H. (2016). Scaling of discrete element model parameters for cohesionless and cohesive solid. Powder Technology, 293, 130–137.

Wet Mixing

Krenzer, K., Mechtcherine, V., & Palzer, U. (2015). Simulating mixing processes with water addition using DEM – from bulk material to suspension.

Stress Calculation

J. Rojek, G.F. Karlis, L.J. Malinowski, G. Beer (2013), Setting up virgin stress conditions in discrete element models. Computers and Geotechnics 48: p. 228-248



The initial implementation of Sphero-Cylinders was done in collaboration with Dr S.A. Papanicolopulos, Senior Lecturer at the School of Engineering of the University of Edinburgh, with support from the Industrial Fellowship scheme of the Royal Academy of Engineering.



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