A normal contact force approach for viscoelastic spheres of the same material

Cundall, 1979, Discrete numerical-model for granular assemblies, Geotechnique, 29, 47, 10.1680/geot.1979.29.1.47 Tsuji, 1992, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technol., 71, 239, 10.1016/0032-5910(92)88030-L Tsuji, 1993, Discrete particle simulation of two dimensional fluidized bed, Powder Technol., 77, 79, 10.1016/0032-5910(93)85010-7 Olsson, 2012, On the effect of particle size distribution in cold powder compaction, ASME. J. Appl. Mech., 79, 10.1115/1.4006382 Olsson, 2013, A numerical analysis of cold powder compaction based on micromechanical experiments, Powder Technol., 243, 71, 10.1016/j.powtec.2013.03.040 Weerasekara, 2013, The contribution of DEM to the science of comminution, Powder Technol., 248, 3, 10.1016/j.powtec.2013.05.032 Fairhurst, 2017, Some challenges of deep mining, Engineering, 3, 527, 10.1016/J.ENG.2017.04.017 Sakai, 2016, How should the discrete element method be applied in industrial systems?: a review, KONA Powder Part. J., 33, 169, 10.14356/kona.2016023 Johnson, 1987 Hunt, 1975, Coefficient of restitution interpreted as damping in vibroimpact, J. Appl. Mech., 42, 440, 10.1115/1.3423596 Zhang, 1996, The calculation of contact forces between particles using spring and damping models, Powder Technol., 88, 59, 10.1016/0032-5910(96)03104-X Hu, 2011, On the determination of the damping coefficient of non-linear spring-dashpot system to model Hertz contact for simulation by discrete element method, J. Comput., 6, 984, 10.4304/jcp.6.5.984-988 Jankowski, 2006, Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding, Earthq. Eng. Struct. Dyn., 35, 517, 10.1002/eqe.537 Kruggel-Emden, 2007, Review and extension of normal force models for the discrete element method, Powder Technol., 171, 157, 10.1016/j.powtec.2006.10.004 Zdancevicius, 2017, Improvement of viscoelastic damping for the Hertz contact of particles due to impact velocity, Procedia Eng., 172, 1286, 10.1016/j.proeng.2017.02.156 Landau, 1986 Lee, 1960, The contact problem for viscoelastic bodies, J. Appl. Mech., 27, 438, 10.1115/1.3644020 Hunter, 1960, The Hertz problem for a rigid spherical indenter and a viscoelastic half-space, J. Mech. Phys. Solids, 8, 219, 10.1016/0022-5096(60)90028-4 Graham, 1965, The contact problem in the linear theory of viscoelasticity, Int. J. Eng. Sci., 3, 27, 10.1016/0020-7225(65)90018-2 Calvit, 1967, Numerical solution of the problem of impact of a rigid sphere onto a linear viscoelastic half-space and comparison with experiment, Int. J. Solids Struct., 3, 951, 10.1016/0020-7683(67)90021-2 Olsson, 2019, A contact model for the normal force between viscoelastic particles in discrete element simulations, Powder Technol., 342, 985, 10.1016/j.powtec.2018.10.022 Kuwabara, 1987, Restitution coefficient in a collision between two spheres, Jpn. J. Appl. Phys., 26, 1230, 10.1143/JJAP.26.1230 Brilliantov, 1996, Model for collisions in granular gases, Phys. Rev. E, 53, 5382, 10.1103/PhysRevE.53.5382 Zheng, 2012, Finite element analysis of the contact forces between a viscoelastic sphere and rigid plane, Powder Technol., 226, 130, 10.1016/j.powtec.2012.04.032 Brilliantov, 2015, A dissipative force between colliding viscoelastic bodies: rigorous approach, EPL (Europhys. Lett.), 109, 10.1209/0295-5075/109/14005 Christensen, 1982 Cross, 1999, The bounce of a ball, Am. J. Phys., 67, 222, 10.1119/1.19229 Gurtin, 1962, On the linear theory of viscoelasticity, Arch. Ration. Mech. An., 11, 291, 10.1007/BF00253942 Lee, 1963, Solution of viscoelastic stress analysis problems using measured creep or relaxation functions, J. Appl. Mech., 30, 127, 10.1115/1.3630057