Molecular Dynamics of Arbitrarily Shaped Granular Particles (original) (raw)
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Engineering-mechanics contact models are utilized to describe the inelastic, frictional interparticle forces acting in dry granular systems. Simple analyses based on one-dimensional chains are utilized to illustrate wave propagation phenomena in dense and dilute discrete particulates. The variation of restitution coefficient with impact velocity is illustrated for a variety of viscous and hysteretiC normal force models. The effects of interparticle friction on material strength in discrete-particle simulations are much closer to measured values than are theories that do not allow particle rotations.
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Physica A: Statistical Mechanics and its Applications, 1999
Kinetic theory of granular media based on inelastic hard sphere interactions predicts continuum equations of motion similar to Navier-Stokes equations for uids. We test these predictions using event-driven molecular dynamics simulations of uniformly excited inelastic hard spheres conÿned to move in a plane. The event-driven simulations have been previously shown to quantitatively reproduce the complex patterns that develop in shallow layers of vertically oscillated granular media. The test system consists of a periodic two-dimensional box ÿlled with inelastic hard disks uniformly forced by small random accelerations in the absence of gravity. We describe the inelasticity of the particles by a velocity-dependent coe cient of restitution. Granular kinetic theory assumes that the velocities at collision are uncorrelated and close to a Maxwell-Boltzmann distribution. Our two-dimensional simulations verify that the velocity distribution is close to a Maxwell-Boltzmann distribution over 3 orders of magnitude in velocity, but we ÿnd that velocity correlations, of up to 40% of the temperature, exist between the velocity components parallel to the relative collision velocity. Despite the velocity correlations we ÿnd that the calculated transport coe cients compare well with kinetic theory predictions.
Transport coefficients for granular media from molecular dynamics simulations
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Under many conditions, macroscopic grains flow like a fluid; kinetic theory predicts continuum equations of motion for this granular fluid. In order to test the theory, we perform event-driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity. ͓S1063-651X͑99͒03310-3͔
Dynamic simulation of the formation of granular media and study of their properties
A numerical model is presented which describes the evolution of a system containing a large number of deformable spherical grains based on Newton's second law. Starting from an initial state with fixed positions, velocities and grain characteristics, the system evolution is simulated by successive steps. The acceleration of each grain results from the application of an external force and from interactions with other particles. These contact forces are evaluated as functions of the grain deformations during the collisions considered as elastic. The grain bed can be deposited between vertical walls as well as with periodical conditions in the lateral directions. The properties of these packings submitted to mechanical stresses are characterized by using numerical codes which operate on unstructured tetrahedral grids on the scale of the individual grains.
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Proceedings of the Third SPHERIC Workshop, 2008
An SPH model of granular material is described. The model replaces standard SPH particles by small molecules each of which moves as a rigid body. We simulate dry granular materials forming piles and show that they have an angle of repose similar to that in nature. We simulate an avalanche by placing the molecules on a steep hillside and show that the avalanche runs onto a horizontal plane and eventually comes to rest. Finally, we simulate dambreaks using a mixture of granular and liquid SPH particles. The effective viscosity of the mixture increases as the concentration of the granular materials increases. The increase is small for a concentration less than 0.5 but increases very rapidly for concentrations above this. These results are similar to those for a Bingham rheology.