Explicit contact force model for superellipses by Fourier transform and application to superellipse packing

Cundall, 1979, A discrete numerical model for granular assemblies, Geotechnique, 29, 47, 10.1680/geot.1979.29.1.47 Zhu, 2008, Discrete particle simulation of particulate systems: a review of major applications and findings, Chem. Eng. Sci., 63, 5728, 10.1016/j.ces.2008.08.006 Sakai, 2015, Discrete element simulation for the evaluation of solid mixing in an industrial blender, Chem. Eng. J., 279, 821, 10.1016/j.cej.2015.04.130 Basinskas, 2016, Numerical study of the mixing efficiency of a batch mixer using the discrete element method, Powder Technol., 301, 815, 10.1016/j.powtec.2016.07.017 Zhong, 2016, DEM/CFD-DEM modelling of non-spherical particulate systems: theoretical developments and applications, Powder Technol., 302, 108, 10.1016/j.powtec.2016.07.010 Govender, 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, Chem. Eng. Sci., 204, 9, 10.1016/j.ces.2019.03.077 Kureck, 2019, Industrial scale simulations of tablet coating using GPU based DEM: a validation study, Chem. Eng. Sci., 202, 462, 10.1016/j.ces.2019.03.029 Chu, 2016, Applicability of a coarse-grained CFD–DEM model on dense medium cyclone, Miner. Eng., 90, 43, 10.1016/j.mineng.2016.01.020 Zheng, 2014, Why have continuum theories previously failed to describe sandpile formation?, Phys. Rev. Lett., 113, 068001, 10.1103/PhysRevLett.113.068001 Hou, 2019, How to generate valid local quantities of particle-fluid flows for establishing constitutive relations, AIChE J., 10.1002/aic.16690 Zhu, 2007, Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci., 62, 3378, 10.1016/j.ces.2006.12.089 Lu, 2015, Discrete element models for non-spherical particle systems: from theoretical developments to applications, Chem. Eng. Sci., 127, 425, 10.1016/j.ces.2014.11.050 Johnson, 1985 Feng, 2012, Energy-conserving contact interaction models for arbitrarily shaped discrete elements, Comput. Methods Appl. Mech. Eng., 205–208, 169, 10.1016/j.cma.2011.02.010 Feng, 2017, A generic contact detection framework for cylindrical particles in discrete element modelling, Comput. Methods Appl. Mech. Eng., 315, 632, 10.1016/j.cma.2016.11.001 Dong, 2015, A novel method based on orientation discretization for discrete element modeling of non-spherical particles, Chem. Eng. Sci., 126, 500, 10.1016/j.ces.2014.12.059 Favier, 1999, Shape representation of axi-symmetrical, non-spherical particles in discrete element simulation using multi-element model particles, Eng. Comput., 16, 467, 10.1108/02644409910271894 Vu-Quoc, 2000, A 3-D discrete-element method for dry granular flows of ellipsoidal particles, Comput. Methods Appl. Mech. Eng., 187, 483, 10.1016/S0045-7825(99)00337-0 Kodam, 2010, Cylindrical object contact detection for use in discrete element method simulations. Part I – contact detection algorithms, Chem. Eng. Sci., 65, 5852, 10.1016/j.ces.2010.08.006 Vorobiev, 2012, Simple common plane contact algorithm, Int. J. Numer. Methods Eng., 90, 243, 10.1002/nme.3324 Nezami, 2004, A fast contact detection algorithm for 3-D discrete element method, Comput. Geotech., 31, 575, 10.1016/j.compgeo.2004.08.002 Wachs, 2012, Grains3D, A flexible DEM approach for particles of arbitrary convex shape — Part I: numerical model and validations, Powder Technol., 224, 374, 10.1016/j.powtec.2012.03.023 Lin, 1995, Contact detection algorithms for three-dimensional ellipsoids in discrete element modelling, Int. J. Numer. Anal. Methods Geomech., 19, 653, 10.1002/nag.1610190905 Zhou, 2011, Dynamic simulation of the packing of ellipsoidal particles, Ind. Eng. Chem. Res., 50, 9787, 10.1021/ie200862n Podlozhnyuk, 2017, Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework, Comput. Part. Mech., 4, 101, 10.1007/s40571-016-0131-6 Houlsby, 2009, Potential particles: a method for modelling non-circular particles in DEM, Comput. Geotech., 36, 953, 10.1016/j.compgeo.2009.03.001 Boon, 2012 Cleary, 1997, Efficient collision detection for three dimensional super-ellipsoidal particles Wellmann, 2008, A contact detection algorithm for superellipsoids based on the common-normal concept, Eng. Comput., 25, 432, 10.1108/02644400810881374 Kildashti, 2018, A revisit of common normal method for discrete modelling of non-spherical particles, Powder Technol., 326, 1, 10.1016/j.powtec.2017.11.066 Cleary, 2000, DEM simulation of industrial particle flows: case studies of dragline excavators, mixing in tumblers and centrifugal mills, Powder Technol., 109, 83, 10.1016/S0032-5910(99)00229-6 Jiang, 2011, Self-assembly of particles: some thoughts and comments, J. Mater. Chem., 21, 16797, 10.1039/c1jm12213d Wu, 2016, The structure and dynamics of higher-order assemblies: amyloids, signalosomes, and granules, Cell, 165, 1055, 10.1016/j.cell.2016.05.004 Kildashti, 2019, Explicit force model for discrete modelling of elliptical particles, Comput. Geotech., 110, 122, 10.1016/j.compgeo.2019.02.004 Shen, 2009, Modeling three-dimensional morphological structures using spherical harmonics, Evolution: Int. J. Org. Evol., 63, 1003, 10.1111/j.1558-5646.2008.00557.x Delaney, 2010, The packing properties of superellipsoids, Europhys. Lett., 89, 34002, 10.1209/0295-5075/89/34002 Donev, 2004, Improving the density of jammed disordered packings using ellipsoids, Science, 303, 990, 10.1126/science.1093010 Delaney, 2011, Defining random loose packing for nonspherical grains, Phys. Rev. E, 83, 051305, 10.1103/PhysRevE.83.051305 Wang, 2015, Structural characterization of the packings of granular regular polygons, Phys. Rev. E, 92, 062203, 10.1103/PhysRevE.92.062203 Zhao, 2012, Dense random packings of spherocylinders, Soft Matter, 8, 1003, 10.1039/C1SM06487H Meng, 2016, Maximally dense random packings of spherocylinders, Powder Technol., 292, 176, 10.1016/j.powtec.2016.01.036 Jaklič, 2000, Superquadrics and their geometric properties, 13 Wikipedia Zhao, 2019, A poly-superellipsoid-based approach on particle morphology for DEM modeling of granular media, Int. J. Numer. Anal. Methods Geomech., 43, 2147, 10.1002/nag.2951 Kildashti, 2018, Evaluation of contact force models for discrete modelling of ellipsoidal particles, Chem. Eng. Sci., 177, 1, 10.1016/j.ces.2017.11.004 Dong, 2016, Voronoi analysis of the packings of non-spherical particles, Chem. Eng. Sci., 153, 330, 10.1016/j.ces.2016.07.013 Džiugys, 2001, An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers, Granul. Matter, 3, 231, 10.1007/PL00010918 Guises, 2009, Granular packing: numerical simulation and the characterisation of the effect of particle shape, Granul. Matter, 11, 281, 10.1007/s10035-009-0148-0 Donev, 2004, Unusually dense crystal packings of ellipsoids, Phys. Rev. Lett., 92, 255506, 10.1103/PhysRevLett.92.255506 Zou, 1996, Evaluation of the packing characteristics of mono-sized non-spherical particles, Powder Technol., 88, 71, 10.1016/0032-5910(96)03106-3