Metaball based discrete element method for general shaped particles with round features

Discrete element method (DEM) has achieved considerable success on simulating complex granular material behaviours. One of the key challenges of DEM simulations is how to describe particles with realistic geometries. Many shape description methods have been developed including sphere-clustering, polyhedrons, sphero-polyhedrons, superquadric particles to name a few. However, to model general shaped particles with round features , these techniques are either introducing artificial surface roughness or are limited to a few regular shapes. Here we proposed a metaball based DEM where the metaball equation is used to describe particle shapes. Because of its flexibility on choosing control points in the metaball equation, many complex shaped particles can be modelled within this framework. The particle collision is handled by solving an optimization problem. A Newton–Raphson method based algorithm of finding the closest points for metaball DEM is developed accordingly. Using 3D printed particles, the proposed scheme is validated by comparing the simulated ran-out distance with granular column collapses experimental results. The model is further applied to study shape effects on vibration induced segregations. It is shown that the proposed metaball DEM can capture shape influence which may crucial in many engineering and science applications.

[1]  Stefan Pirker,et al.  Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework , 2017, CPM 2017.

[2]  Fernando Alonso-Marroquin,et al.  Spheropolygons: A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies , 2008 .

[3]  Guilhem Mollon,et al.  Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials , 2012, Granular Matter.

[4]  Y C Wang,et al.  Molecular dynamics simulation of complex particles in three dimensions and the study of friction due to nonconvexity. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Andrei V. Lyamin,et al.  Granular contact dynamics using mathematical programming methods , 2012 .

[6]  Nivedita Das,et al.  Modeling Three-Dimensional Shape of Sand Grains Using Discrete Element Method , 2007 .

[7]  Ilia A. Solov’yov,et al.  MBN Explorer Users' Guide , 2017 .

[8]  John R. Williams,et al.  SUPERQUADRICS AND MODAL DYNAMICS FOR DISCRETE ELEMENTS IN INTERACTIVE DESIGN , 1992 .

[9]  Guy T. Houlsby,et al.  Potential particles: a method for modelling non-circular particles in DEM , 2009 .

[10]  José E. Andrade,et al.  Granular Element Method for Computational Particle Mechanics , 2012 .

[11]  S. Luding.  Introduction to discrete element methods , 2008 .

[12]  Harald Kruggel-Emden,et al.  A study on the validity of the multi-sphere Discrete Element Method , 2008 .

[13]  A. Scheuermann,et al.  Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles. , 2016, Physical review. E.

[14]  S. Luding.  Cohesive, frictional powders: contact models for tension , 2008 .

[15]  Jiansheng Xiang,et al.  A clustered overlapping sphere algorithm to represent real particles in discrete element modelling , 2009 .

[16]  Jinyang Zheng,et al.  Diffusion of size bidisperse spheres in dense granular shear flow. , 2019, Physical review. E.

[17]  S. Galindo-Torres,et al.  Molecular dynamics simulations of complex shaped particles using Minkowski operators , 2008, 0811.2858.

[18]  Colin Webb,et al.  Experimental validation of polyhedral discrete element model , 2011 .

[19]  S. Galindo-Torres,et al.  Smooth particle hydrodynamics and discrete element method coupling scheme for the simulation of debris flows , 2020 .

[20]  Jidong Zhao,et al.  3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors , 2014 .

[21]  C. Lacoursière,et al.  Examining the smooth and nonsmooth discrete element approaches to granular matter , 2014 .

[22]  John T Harvey,et al.  Polyarc discrete element for efficiently simulating arbitrarily shaped 2D particles , 2012 .

[23]  Qiushi Chen,et al.  Fourier series-based discrete element method for computational mechanics of irregular-shaped particles , 2020, Computer Methods in Applied Mechanics and Engineering.

[24]  Ling Li,et al.  Breaking processes in three-dimensional bonded granular materials with general shapes , 2012, Comput. Phys. Commun..

[25]  Sergio Andres Galindo-Torres,et al.  A coupled Discrete Element Lattice Boltzmann Method for the simulation of fluid-solid interaction with particles of general shapes , 2013 .

[26]  G. Houlsby,et al.  A new contact detection algorithm for three-dimensional non-spherical particles , 2013 .

[27]  Fernando Alonso-Marroquín,et al.  An efficient algorithm for granular dynamics simulations with complex-shaped objects , 2008 .

[28]  Shiwei Zhao,et al.  A poly‐superellipsoid‐based approach on particle morphology for DEM modeling of granular media , 2019, International Journal for Numerical and Analytical Methods in Geomechanics.

[29]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[30]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[31]  Harald Kruggel-Emden,et al.  Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts , 2011 .

[32]  J.A.M. Kuipers,et al.  A granular Discrete Element Method for arbitrary convex particle shapes: Method and packing generation , 2018, Chemical Engineering Science.

[33]  K. Soga,et al.  Particle shape characterisation using Fourier descriptor analysis , 2001 .

[34]  Chuan-Yu Wu,et al.  Numerical and experimental investigations of the flow of powder into a confined space , 2006 .

[35]  C. Kwok,et al.  Micromechanical Origin of Particle Size Segregation. , 2017, Physical review letters.

[36]  J. Bullard,et al.  Contact function, uniform-thickness shell volume, and convexity measure for 3D star-shaped random particles , 2013 .

[37]  Yannick Descantes,et al.  Classical contact detection algorithms for 3D DEM simulations: Drawbacks and solutions , 2019, Computers and Geotechnics.

[38]  J. D. Muñoz,et al.  Minkowski-Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  S. Galindo-Torres,et al.  An efficient Discrete Element Lattice Boltzmann model for simulation of particle-fluid, particle-particle interactions , 2017 .

[40]  Paul W. Cleary,et al.  DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge , 2002 .