Towards dense, realistic granular media in 2D

The development of an applicable theory for granular matter - with both qualitative and quantitative value - is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.\ud \ud In most systems, low density co-exists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional nonlinear phenomena and material properties are important in realistic granular media, involving, e.g.:\ud \ud (i) multi-particle interactions and elasticity\ud (ii) strong dissipation,\ud (iii) friction,\ud (iv) long-range forces and wet contacts,\ud (v) wide particle size distributions and\ud (vi) various particle shapes.\ud \ud \ud Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some cannot.\ud \ud This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions and corrections given are qualitatively true also in 3D.\ud \ud Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier–Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws - one by one - in order to account for the realistic physical effects and properties listed above

Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media

In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading to even stronger dissipation and thus causing the density instability. The assumption of `molecular chaos' is valid only in the homogeneous cooling regime. As soon as the density instability occurs, the impact parameter is not longer uniformly distributed. The pair-correlation and the structure functions show that the molecular chaos assumption --- together with reasonable excluded volume modeling --- is important for short distances and irrelevant on large length scales. In this study, the probability distribution of the collision frequency is examined for pipe flow and for freely cooling granular materials as well. Uncorrelated events lead to a Poisson distribution for the collision frequencies. In contrast, the fingerprint of the cooperative phenomena discussed here is a power-law decay of the probability for many collisions per unit time. Keywords: discrete element method, event driven simulations, clustering instability, arching, shock waves, power-law distribution, cooperative phenomena.Comment: 27 pages 14 figs (2 color

Cohesive, frictional powders: contact models for tension

The contacts between cohesive, frictional particles with sizes in the range 0.1–10 μm are the subject of this study. Discrete element model (DEM) simulations rely on realistic contact force models—however, too much details make both implementation and interpretation prohibitively difficult. A rather simple, objective contact model is presented, involving the physical properties of elastic–plastic repulsion, dissipation, adhesion, friction as well as rolling- and torsion-resistance. This contact model allows to model bulk properties like friction, cohesion and yield-surfaces. Very loose packings and even fractal agglomerates have been reported in earlier work. The same model also allows for pressure-sintering and tensile strength tests as presented in this study

Consequences of using different pair-correlation functions on the stability properties of the Homogeneous Cooling State for a monodisperse system of near-elastic disks

We show the differences in the stability properties of the Homogeneous Cooling State (HCS) of a two-dimensional monodisperse collection of rigid and near-elastic disks, obtained by using different formulae for the pair-correlation function.For an equation of state that takes into account the crystallization and ordering of the particles (and the respective pressure drop), the critical wavelength of the heat conduction mode is considerably modified in the transition zone, involving a bifurcation and an additional mode of instability. The theoretical predictions, using the improved equation of state are confirmed by numerical simulations. Nevertheless, some open questions remain

How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model

The inelastic hard sphere model of granular material is simple, easily accessible to theory and simulation, and captures much of the physics of granular media. It has three drawbacks, all related to the approximation that collisions are instantaneous: 1) The number of collisions per unit time can diverge, i.e. the ``inelastic collapse'' can occur. 2) All interactions are binary, multiparticle contacts cannot occur and 3) no static limit exists. We extend the inelastic hard sphere model by defining a duration of contact t_c such that dissipation is allowed only if the time between contacts is larger than t_c. We name this generalized model the ``TC model'' and discuss it using examples of dynamic and static systems. The contact duration used here does not change the instantaneous nature of the hard sphere contacts, but accounts for a reduced dissipation during ``multiparticle contacts''. Kinetic and elastic energies are defined as well as forces and stresses in the system. Finally, we present event-driven numerical simulations of situations far beyond the inelastic collapse, possible only with the TC model.Comment: 15 pages, Latex, 14 bw.ps figures + 2 col.ps figures, to be published in Granular Matter 1(3) 199

Evolution of swelling pressure of cohesive-frictional, rough and elasto-plastic granulates

The subject of this study is the modeling of the evolution of the swell-ing pressure of granulates with cohesive-frictional, rough and elasto-plastic “mi-croscopic” contact properties. The spherical particles are randomly arranged in a periodic cubic space with a fixed volume so that an increase of the particle size – i.e. swelling that can be caused by intake of some fluid – is accompanied by a de-crease of the void space. An analytical function is proposed that properly de-scribes the (macroscopic) void ratio as function of pressure for different micro-scopic contact properties